LMFDB - Embedded newform 961.2.d.c.374.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(374,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.374"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.d (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,-3,6,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			374.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	961.374
Dual form			961.2.d.c.388.1

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.30902 - 0.951057i) q^{2} +(2.61803 - 1.90211i) q^{3} +(0.190983 + 0.587785i) q^{4} +1.00000 q^{5} -5.23607 q^{6} +(0.0729490 + 0.224514i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(2.30902 - 7.10642i) q^{9} +(-1.30902 - 0.951057i) q^{10} +(0.618034 + 1.90211i) q^{11} +(1.61803 + 1.17557i) q^{12} +(2.61803 - 1.90211i) q^{13} +(0.118034 - 0.363271i) q^{14} +(2.61803 - 1.90211i) q^{15} +(3.92705 - 2.85317i) q^{16} +(0.236068 - 0.726543i) q^{17} +(-9.78115 + 7.10642i) q^{18} +(1.80902 + 1.31433i) q^{19} +(0.190983 + 0.587785i) q^{20} +(0.618034 + 0.449028i) q^{21} +(1.00000 - 3.07768i) q^{22} +(1.76393 - 5.42882i) q^{23} +(2.23607 + 6.88191i) q^{24} -4.00000 q^{25} -5.23607 q^{26} +(-4.47214 - 13.7638i) q^{27} +(-0.118034 + 0.0857567i) q^{28} +(-2.23607 - 1.62460i) q^{29} -5.23607 q^{30} -3.38197 q^{32} +(5.23607 + 3.80423i) q^{33} +(-1.00000 + 0.726543i) q^{34} +(0.0729490 + 0.224514i) q^{35} +4.61803 q^{36} -2.00000 q^{37} +(-1.11803 - 3.44095i) q^{38} +(3.23607 - 9.95959i) q^{39} +(-0.690983 + 2.12663i) q^{40} +(-5.66312 - 4.11450i) q^{41} +(-0.381966 - 1.17557i) q^{42} +(-1.00000 - 0.726543i) q^{43} +(-1.00000 + 0.726543i) q^{44} +(2.30902 - 7.10642i) q^{45} +(-7.47214 + 5.42882i) q^{46} +(-2.00000 + 1.45309i) q^{47} +(4.85410 - 14.9394i) q^{48} +(5.61803 - 4.08174i) q^{49} +(5.23607 + 3.80423i) q^{50} +(-0.763932 - 2.35114i) q^{51} +(1.61803 + 1.17557i) q^{52} +(-3.23607 + 9.95959i) q^{53} +(-7.23607 + 22.2703i) q^{54} +(0.618034 + 1.90211i) q^{55} -0.527864 q^{56} +7.23607 q^{57} +(1.38197 + 4.25325i) q^{58} +(-1.80902 + 1.31433i) q^{59} +(1.61803 + 1.17557i) q^{60} +8.18034 q^{61} +1.76393 q^{63} +(-3.42705 - 2.48990i) q^{64} +(2.61803 - 1.90211i) q^{65} +(-3.23607 - 9.95959i) q^{66} +8.00000 q^{67} +0.472136 q^{68} +(-5.70820 - 17.5680i) q^{69} +(0.118034 - 0.363271i) q^{70} +(-2.83688 + 8.73102i) q^{71} +(13.5172 + 9.82084i) q^{72} +(2.61803 + 8.05748i) q^{73} +(2.61803 + 1.90211i) q^{74} +(-10.4721 + 7.60845i) q^{75} +(-0.427051 + 1.31433i) q^{76} +(-0.381966 + 0.277515i) q^{77} +(-13.7082 + 9.95959i) q^{78} +(-3.61803 + 11.1352i) q^{79} +(3.92705 - 2.85317i) q^{80} +(-19.7533 - 14.3516i) q^{81} +(3.50000 + 10.7719i) q^{82} +(12.0902 + 8.78402i) q^{83} +(-0.145898 + 0.449028i) q^{84} +(0.236068 - 0.726543i) q^{85} +(0.618034 + 1.90211i) q^{86} -8.94427 q^{87} -4.47214 q^{88} +(3.61803 + 11.1352i) q^{89} +(-9.78115 + 7.10642i) q^{90} +(0.618034 + 0.449028i) q^{91} +3.52786 q^{92} +4.00000 q^{94} +(1.80902 + 1.31433i) q^{95} +(-8.85410 + 6.43288i) q^{96} +(-4.92705 - 15.1639i) q^{97} -11.2361 q^{98} +14.9443 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} + 6 q^{3} + 3 q^{4} + 4 q^{5} - 12 q^{6} + 7 q^{7} - 5 q^{8} + 7 q^{9} - 3 q^{10} - 2 q^{11} + 2 q^{12} + 6 q^{13} - 4 q^{14} + 6 q^{15} + 9 q^{16} - 8 q^{17} - 19 q^{18} + 5 q^{19} + 3 q^{20}+ \cdots + 24 q^{99}+O(q^{100}) $ 4 * q - 3 * q^2 + 6 * q^3 + 3 * q^4 + 4 * q^5 - 12 * q^6 + 7 * q^7 - 5 * q^8 + 7 * q^9 - 3 * q^10 - 2 * q^11 + 2 * q^12 + 6 * q^13 - 4 * q^14 + 6 * q^15 + 9 * q^16 - 8 * q^17 - 19 * q^18 + 5 * q^19 + 3 * q^20 - 2 * q^21 + 4 * q^22 + 16 * q^23 - 16 * q^25 - 12 * q^26 + 4 * q^28 - 12 * q^30 - 18 * q^32 + 12 * q^33 - 4 * q^34 + 7 * q^35 + 14 * q^36 - 8 * q^37 + 4 * q^39 - 5 * q^40 - 7 * q^41 - 6 * q^42 - 4 * q^43 - 4 * q^44 + 7 * q^45 - 12 * q^46 - 8 * q^47 + 6 * q^48 + 18 * q^49 + 12 * q^50 - 12 * q^51 + 2 * q^52 - 4 * q^53 - 20 * q^54 - 2 * q^55 - 20 * q^56 + 20 * q^57 + 10 * q^58 - 5 * q^59 + 2 * q^60 - 12 * q^61 + 16 * q^63 - 7 * q^64 + 6 * q^65 - 4 * q^66 + 32 * q^67 - 16 * q^68 + 4 * q^69 - 4 * q^70 - 27 * q^71 + 25 * q^72 + 6 * q^73 + 6 * q^74 - 24 * q^75 + 5 * q^76 - 6 * q^77 - 28 * q^78 - 10 * q^79 + 9 * q^80 - 41 * q^81 + 14 * q^82 + 26 * q^83 - 14 * q^84 - 8 * q^85 - 2 * q^86 + 10 * q^89 - 19 * q^90 - 2 * q^91 + 32 * q^92 + 16 * q^94 + 5 * q^95 - 22 * q^96 - 13 * q^97 - 36 * q^98 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.30902	−	0.951057i	−0.925615	−	0.672499i	0.0193004	−	0.999814i	$-0.493856\pi$
$2$	−1.30902	−	0.951057i	−0.925615	−	0.672499i	−0.944915	+	0.327315i	$0.893856\pi$
$3$	2.61803	−	1.90211i	1.51152	−	1.09819i	0.546027	−	0.837768i	$-0.316140\pi$
$3$	2.61803	−	1.90211i	1.51152	−	1.09819i	0.965496	−	0.260418i	$-0.0838602\pi$
$4$	0.190983	+	0.587785i	0.0954915	+	0.293893i
$5$	1.00000			0.447214			0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000			0.447214			0.223607	+	0.974679i	$0.428217\pi$
$6$	−5.23607			−2.13762
$7$	0.0729490	+	0.224514i	0.0275721	+	0.0848583i	0.963896	−	0.266280i	$-0.0857946\pi$
$7$	0.0729490	+	0.224514i	0.0275721	+	0.0848583i	−0.936324	+	0.351138i	$0.885795\pi$
$8$	−0.690983	+	2.12663i	−0.244299	+	0.751876i
$9$	2.30902	−	7.10642i	0.769672	−	2.36881i
$10$	−1.30902	−	0.951057i	−0.413948	−	0.300750i
$11$	0.618034	+	1.90211i	0.186344	+	0.573509i	0.999969	−	0.00788181i	$-0.00250889\pi$
$11$	0.618034	+	1.90211i	0.186344	+	0.573509i	−0.813625	+	0.581390i	$0.802509\pi$
$12$	1.61803	+	1.17557i	0.467086	+	0.339358i
$13$	2.61803	−	1.90211i	0.726112	−	0.527551i	−0.162219	−	0.986755i	$-0.551865\pi$
$13$	2.61803	−	1.90211i	0.726112	−	0.527551i	0.888331	+	0.459204i	$0.151865\pi$
$14$	0.118034	−	0.363271i	0.0315459	−	0.0970883i
$15$	2.61803	−	1.90211i	0.675973	−	0.491123i
$16$	3.92705	−	2.85317i	0.981763	−	0.713292i
$17$	0.236068	−	0.726543i	0.0572549	−	0.176212i	−0.918339	−	0.395794i	$-0.870469\pi$
$17$	0.236068	−	0.726543i	0.0572549	−	0.176212i	0.975594	+	0.219582i	$0.0704693\pi$
$18$	−9.78115	+	7.10642i	−2.30544	+	1.67500i
$19$	1.80902	+	1.31433i	0.415017	+	0.301527i	0.775630	−	0.631188i	$-0.217432\pi$
$19$	1.80902	+	1.31433i	0.415017	+	0.301527i	−0.360613	+	0.932716i	$0.617432\pi$
$20$	0.190983	+	0.587785i	0.0427051	+	0.131433i
$21$	0.618034	+	0.449028i	0.134866	+	0.0979859i
$22$	1.00000	−	3.07768i	0.213201	−	0.656164i
$23$	1.76393	−	5.42882i	0.367805	−	1.13199i	−0.580400	−	0.814331i	$-0.697104\pi$
$23$	1.76393	−	5.42882i	0.367805	−	1.13199i	0.948206	−	0.317657i	$-0.102896\pi$
$24$	2.23607	+	6.88191i	0.456435	+	1.40476i
$25$	−4.00000			−0.800000
$26$	−5.23607			−1.02688
$27$	−4.47214	−	13.7638i	−0.860663	−	2.64885i
$28$	−0.118034	+	0.0857567i	−0.0223063	+	0.0162065i
$29$	−2.23607	−	1.62460i	−0.415227	−	0.301680i	0.360487	−	0.932764i	$-0.382610\pi$
$29$	−2.23607	−	1.62460i	−0.415227	−	0.301680i	−0.775715	+	0.631084i	$0.782610\pi$
$30$	−5.23607			−0.955971
$31$		0			0
$31$		0			0
$32$	−3.38197			−0.597853
$33$	5.23607	+	3.80423i	0.911482	+	0.662231i
$34$	−1.00000	+	0.726543i	−0.171499	+	0.124601i
$35$	0.0729490	+	0.224514i	0.0123306	+	0.0379498i
$36$	4.61803			0.769672
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$	−1.11803	−	3.44095i	−0.181369	−	0.558197i
$39$	3.23607	−	9.95959i	0.518186	−	1.59481i
$40$	−0.690983	+	2.12663i	−0.109254	+	0.336249i
$41$	−5.66312	−	4.11450i	−0.884431	−	0.642576i	0.0499893	−	0.998750i	$-0.484081\pi$
$41$	−5.66312	−	4.11450i	−0.884431	−	0.642576i	−0.934420	+	0.356173i	$0.884081\pi$
$42$	−0.381966	−	1.17557i	−0.0589386	−	0.181394i
$43$	−1.00000	−	0.726543i	−0.152499	−	0.110797i	0.508920	−	0.860814i	$-0.330045\pi$
$43$	−1.00000	−	0.726543i	−0.152499	−	0.110797i	−0.661418	+	0.750017i	$0.730045\pi$
$44$	−1.00000	+	0.726543i	−0.150756	+	0.109530i
$45$	2.30902	−	7.10642i	0.344208	−	1.05936i
$46$	−7.47214	+	5.42882i	−1.10171	+	0.800437i
$47$	−2.00000	+	1.45309i	−0.291730	+	0.211954i	−0.724018	−	0.689782i	$-0.757707\pi$
$47$	−2.00000	+	1.45309i	−0.291730	+	0.211954i	0.432288	+	0.901736i	$0.357707\pi$
$48$	4.85410	−	14.9394i	0.700629	−	2.15632i
$49$	5.61803	−	4.08174i	0.802576	−	0.583106i
$50$	5.23607	+	3.80423i	0.740492	+	0.537999i
$51$	−0.763932	−	2.35114i	−0.106972	−	0.329226i
$52$	1.61803	+	1.17557i	0.224381	+	0.163022i
$53$	−3.23607	+	9.95959i	−0.444508	+	1.36806i	0.438514	+	0.898724i	$0.355505\pi$
$53$	−3.23607	+	9.95959i	−0.444508	+	1.36806i	−0.883022	+	0.469331i	$0.844495\pi$
$54$	−7.23607	+	22.2703i	−0.984704	+	3.03061i
$55$	0.618034	+	1.90211i	0.0833357	+	0.256481i
$56$	−0.527864			−0.0705388
$57$	7.23607			0.958441
$58$	1.38197	+	4.25325i	0.181461	+	0.558480i
$59$	−1.80902	+	1.31433i	−0.235514	+	0.171111i	−0.699282	−	0.714846i	$-0.746497\pi$
$59$	−1.80902	+	1.31433i	−0.235514	+	0.171111i	0.463768	+	0.885956i	$0.346497\pi$
$60$	1.61803	+	1.17557i	0.208887	+	0.151765i
$61$	8.18034			1.04739			0.523693	−	0.851907i	$-0.324554\pi$
$61$	8.18034			1.04739			0.523693	+	0.851907i	$0.324554\pi$
$62$		0			0
$63$	1.76393			0.222235
$64$	−3.42705	−	2.48990i	−0.428381	−	0.311237i
$65$	2.61803	−	1.90211i	0.324727	−	0.235928i
$66$	−3.23607	−	9.95959i	−0.398332	−	1.22594i
$67$	8.00000			0.977356			0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000			0.977356			0.488678	+	0.872464i	$0.337479\pi$
$68$	0.472136			0.0572549
$69$	−5.70820	−	17.5680i	−0.687187	−	2.11494i
$70$	0.118034	−	0.363271i	0.0141078	−	0.0434192i
$71$	−2.83688	+	8.73102i	−0.336676	+	1.03618i	0.629215	+	0.777231i	$0.283377\pi$
$71$	−2.83688	+	8.73102i	−0.336676	+	1.03618i	−0.965891	+	0.258950i	$0.916623\pi$
$72$	13.5172	+	9.82084i	1.59302	+	1.15740i
$73$	2.61803	+	8.05748i	0.306418	+	0.943057i	0.979144	+	0.203166i	$0.0651230\pi$
$73$	2.61803	+	8.05748i	0.306418	+	0.943057i	−0.672727	+	0.739891i	$0.734877\pi$
$74$	2.61803	+	1.90211i	0.304340	+	0.221116i
$75$	−10.4721	+	7.60845i	−1.20922	+	0.878548i
$76$	−0.427051	+	1.31433i	−0.0489861	+	0.150764i
$77$	−0.381966	+	0.277515i	−0.0435291	+	0.0316257i
$78$	−13.7082	+	9.95959i	−1.55215	+	1.12770i
$79$	−3.61803	+	11.1352i	−0.407061	+	1.25280i	0.512102	+	0.858925i	$0.328867\pi$
$79$	−3.61803	+	11.1352i	−0.407061	+	1.25280i	−0.919162	+	0.393879i	$0.871133\pi$
$80$	3.92705	−	2.85317i	0.439058	−	0.318994i
$81$	−19.7533	−	14.3516i	−2.19481	−	1.59462i
$82$	3.50000	+	10.7719i	0.386510	+	1.18956i
$83$	12.0902	+	8.78402i	1.32707	+	0.964172i	0.999815	+	0.0192352i	$0.00612313\pi$
$83$	12.0902	+	8.78402i	1.32707	+	0.964172i	0.327254	+	0.944937i	$0.393877\pi$
$84$	−0.145898	+	0.449028i	−0.0159188	+	0.0489930i
$85$	0.236068	−	0.726543i	0.0256052	−	0.0788046i
$86$	0.618034	+	1.90211i	0.0666443	+	0.205110i
$87$	−8.94427			−0.958927
$88$	−4.47214			−0.476731
$89$	3.61803	+	11.1352i	0.383511	+	1.18032i	0.937555	+	0.347838i	$0.113084\pi$
$89$	3.61803	+	11.1352i	0.383511	+	1.18032i	−0.554044	+	0.832487i	$0.686916\pi$
$90$	−9.78115	+	7.10642i	−1.03102	+	0.749083i
$91$	0.618034	+	0.449028i	0.0647876	+	0.0470709i
$92$	3.52786			0.367805
$93$		0			0
$94$	4.00000			0.412568
$95$	1.80902	+	1.31433i	0.185601	+	0.134847i
$96$	−8.85410	+	6.43288i	−0.903668	+	0.656553i
$97$	−4.92705	−	15.1639i	−0.500266	−	1.53966i	−0.808586	−	0.588378i	$-0.799767\pi$
$97$	−4.92705	−	15.1639i	−0.500266	−	1.53966i	0.308320	−	0.951283i	$-0.400233\pi$
$98$	−11.2361			−1.13501
$99$	14.9443			1.50196
$100$	−0.763932	−	2.35114i	−0.0763932	−	0.235114i
$101$	−0.927051	+	2.85317i	−0.0922450	+	0.283901i	−0.986526	−	0.163605i	$-0.947688\pi$
$101$	−0.927051	+	2.85317i	−0.0922450	+	0.283901i	0.894281	+	0.447506i	$0.147688\pi$
$102$	−1.23607	+	3.80423i	−0.122389	+	0.376675i
$103$	−5.04508	−	3.66547i	−0.497107	−	0.361169i	0.310804	−	0.950474i	$-0.399402\pi$
$103$	−5.04508	−	3.66547i	−0.497107	−	0.361169i	−0.807911	+	0.589305i	$0.799402\pi$
$104$	2.23607	+	6.88191i	0.219265	+	0.674827i
$105$	0.618034	+	0.449028i	0.0603139	+	0.0438206i
$106$	13.7082	−	9.95959i	1.33146	−	0.967361i
$107$	1.78115	−	5.48183i	0.172191	−	0.529948i	−0.827303	−	0.561755i	$-0.810126\pi$
$107$	1.78115	−	5.48183i	0.172191	−	0.529948i	0.999494	+	0.0318072i	$0.0101263\pi$
$108$	7.23607	−	5.25731i	0.696291	−	0.505885i
$109$	11.2812	−	8.19624i	1.08054	−	0.785057i	0.102762	−	0.994706i	$-0.467232\pi$
$109$	11.2812	−	8.19624i	1.08054	−	0.785057i	0.977777	+	0.209649i	$0.0672321\pi$
$110$	1.00000	−	3.07768i	0.0953463	−	0.293446i
$111$	−5.23607	+	3.80423i	−0.496986	+	0.361081i
$112$	0.927051	+	0.673542i	0.0875981	+	0.0636437i
$113$	1.07295	+	3.30220i	0.100935	+	0.310645i	0.988755	−	0.149546i	$-0.0477811\pi$
$113$	1.07295	+	3.30220i	0.100935	+	0.310645i	−0.887820	+	0.460190i	$0.847781\pi$
$114$	−9.47214	−	6.88191i	−0.887147	−	0.644550i
$115$	1.76393	−	5.42882i	0.164488	−	0.506240i
$116$	0.527864	−	1.62460i	0.0490109	−	0.150840i
$117$	−7.47214	−	22.9969i	−0.690799	−	2.12606i
$118$	3.61803			0.333067
$119$	0.180340			0.0165317
$120$	2.23607	+	6.88191i	0.204124	+	0.628230i
$121$	5.66312	−	4.11450i	0.514829	−	0.374045i
$122$	−10.7082	−	7.77997i	−0.969475	−	0.704365i
$123$	−22.6525			−2.04250
$124$		0			0
$125$	−9.00000			−0.804984
$126$	−2.30902	−	1.67760i	−0.205704	−	0.149452i
$127$	−10.0902	+	7.33094i	−0.895358	+	0.650516i	−0.937269	−	0.348606i	$-0.886655\pi$
$127$	−10.0902	+	7.33094i	−0.895358	+	0.650516i	0.0419116	+	0.999121i	$0.486655\pi$
$128$	4.20820	+	12.9515i	0.371956	+	1.14476i
$129$	−4.00000			−0.352180
$130$	−5.23607			−0.459234
$131$	3.70820	+	11.4127i	0.323987	+	0.997130i	0.971896	+	0.235412i	$0.0756440\pi$
$131$	3.70820	+	11.4127i	0.323987	+	0.997130i	−0.647908	+	0.761718i	$0.724356\pi$
$132$	−1.23607	+	3.80423i	−0.107586	+	0.331115i
$133$	−0.163119	+	0.502029i	−0.0141442	+	0.0435314i
$134$	−10.4721	−	7.60845i	−0.904655	−	0.657270i
$135$	−4.47214	−	13.7638i	−0.384900	−	1.18460i
$136$	1.38197	+	1.00406i	0.118503	+	0.0860972i
$137$	−5.09017	+	3.69822i	−0.434883	+	0.315961i	−0.783598	−	0.621268i	$-0.786618\pi$
$137$	−5.09017	+	3.69822i	−0.434883	+	0.315961i	0.348716	+	0.937229i	$0.386618\pi$
$138$	−9.23607	+	28.4257i	−0.786226	+	2.41976i
$139$	−10.8541	+	7.88597i	−0.920633	+	0.668879i	−0.943681	−	0.330855i	$-0.892663\pi$
$139$	−10.8541	+	7.88597i	−0.920633	+	0.668879i	0.0230486	+	0.999734i	$0.492663\pi$
$140$	−0.118034	+	0.0857567i	−0.00997569	+	0.00724777i
$141$	−2.47214	+	7.60845i	−0.208191	+	0.640747i
$142$	12.0172	−	8.73102i	1.00846	−	0.732691i
$143$	5.23607	+	3.80423i	0.437862	+	0.318125i
$144$	−11.2082	−	34.4953i	−0.934017	−	2.87461i
$145$	−2.23607	−	1.62460i	−0.185695	−	0.134916i
$146$	4.23607	−	13.0373i	0.350579	−	1.07897i
$147$	6.94427	−	21.3723i	0.572754	−	1.76276i
$148$	−0.381966	−	1.17557i	−0.0313974	−	0.0966313i
$149$	10.0000			0.819232			0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000			0.819232			0.409616	+	0.912258i	$0.365663\pi$
$150$	20.9443			1.71009
$151$	−4.38197	−	13.4863i	−0.356599	−	1.09750i	−0.955076	−	0.296360i	$-0.904227\pi$
$151$	−4.38197	−	13.4863i	−0.356599	−	1.09750i	0.598477	−	0.801140i	$-0.295773\pi$
$152$	−4.04508	+	2.93893i	−0.328100	+	0.238378i
$153$	−4.61803	−	3.35520i	−0.373346	−	0.271252i
$154$	0.763932			0.0615594
$155$		0			0
$156$	6.47214			0.518186
$157$	−16.8992	−	12.2780i	−1.34870	−	0.979889i	−0.999075	−	0.0430003i	$-0.986308\pi$
$157$	−16.8992	−	12.2780i	−1.34870	−	0.979889i	−0.349627	−	0.936889i	$-0.613692\pi$
$158$	15.3262	−	11.1352i	1.21929	−	0.885866i
$159$	10.4721	+	32.2299i	0.830494	+	2.55600i
$160$	−3.38197			−0.267368
$161$	1.34752			0.106200
$162$	12.2082	+	37.5730i	0.959167	+	2.95201i
$163$	3.30902	−	10.1841i	0.259182	−	0.797681i	−0.733795	−	0.679371i	$-0.762253\pi$
$163$	3.30902	−	10.1841i	0.259182	−	0.797681i	0.992977	−	0.118309i	$-0.0377475\pi$
$164$	1.33688	−	4.11450i	0.104393	−	0.321288i
$165$	5.23607	+	3.80423i	0.407627	+	0.296159i
$166$	−7.47214	−	22.9969i	−0.579950	−	1.78490i
$167$	5.23607	+	3.80423i	0.405179	+	0.294380i	0.771647	−	0.636051i	$-0.219433\pi$
$167$	5.23607	+	3.80423i	0.405179	+	0.294380i	−0.366468	+	0.930431i	$0.619433\pi$
$168$	−1.38197	+	1.00406i	−0.106621	+	0.0774647i
$169$	−0.781153	+	2.40414i	−0.0600887	+	0.184934i
$170$	−1.00000	+	0.726543i	−0.0766965	+	0.0557233i
$171$	13.5172	−	9.82084i	1.03369	−	0.751018i
$172$	0.236068	−	0.726543i	0.0180000	−	0.0553983i
$173$	−2.38197	+	1.73060i	−0.181098	+	0.131575i	−0.674641	−	0.738146i	$-0.735701\pi$
$173$	−2.38197	+	1.73060i	−0.181098	+	0.131575i	0.493543	+	0.869721i	$0.335701\pi$
$174$	11.7082	+	8.50651i	0.887597	+	0.644877i
$175$	−0.291796	−	0.898056i	−0.0220577	−	0.0678866i
$176$	7.85410	+	5.70634i	0.592025	+	0.430131i
$177$	−2.23607	+	6.88191i	−0.168073	+	0.517276i
$178$	5.85410	−	18.0171i	0.438783	−	1.35044i
$179$	0.527864	+	1.62460i	0.0394544	+	0.121428i	0.968844	−	0.247673i	$-0.0796657\pi$
$179$	0.527864	+	1.62460i	0.0394544	+	0.121428i	−0.929389	+	0.369101i	$0.879666\pi$
$180$	4.61803			0.344208
$181$	−4.18034			−0.310722			−0.155361	−	0.987858i	$-0.549654\pi$
$181$	−4.18034			−0.310722			−0.155361	+	0.987858i	$0.549654\pi$
$182$	−0.381966	−	1.17557i	−0.0283132	−	0.0871391i
$183$	21.4164	−	15.5599i	1.58315	−	1.15022i
$184$	10.3262	+	7.50245i	0.761260	+	0.553088i
$185$	−2.00000			−0.147043
$186$		0			0
$187$	1.52786			0.111728
$188$	−1.23607	−	0.898056i	−0.0901495	−	0.0654975i
$189$	2.76393	−	2.00811i	0.201046	−	0.146069i
$190$	−1.11803	−	3.44095i	−0.0811107	−	0.249633i
$191$	−19.1803			−1.38784			−0.693920	−	0.720052i	$-0.744118\pi$
$191$	−19.1803			−1.38784			−0.693920	+	0.720052i	$0.744118\pi$
$192$	−13.7082			−0.989304
$193$	1.07295	+	3.30220i	0.0772326	+	0.237697i	0.982218	−	0.187746i	$-0.0601182\pi$
$193$	1.07295	+	3.30220i	0.0772326	+	0.237697i	−0.904985	+	0.425443i	$0.860118\pi$
$194$	−7.97214	+	24.5357i	−0.572366	+	1.76156i
$195$	3.23607	−	9.95959i	0.231740	−	0.713221i
$196$	3.47214	+	2.52265i	0.248010	+	0.180190i
$197$	3.52786	+	10.8576i	0.251350	+	0.773575i	0.994527	+	0.104481i	$0.0333180\pi$
$197$	3.52786	+	10.8576i	0.251350	+	0.773575i	−0.743177	+	0.669095i	$0.766682\pi$
$198$	−19.5623	−	14.2128i	−1.39023	−	1.01006i
$199$	15.3262	−	11.1352i	1.08645	−	0.789351i	0.107652	−	0.994189i	$-0.465667\pi$
$199$	15.3262	−	11.1352i	1.08645	−	0.789351i	0.978796	+	0.204838i	$0.0656667\pi$
$200$	2.76393	−	8.50651i	0.195440	−	0.601501i
$201$	20.9443	−	15.2169i	1.47730	−	1.07332i
$202$	3.92705	−	2.85317i	0.276306	−	0.200748i
$203$	0.201626	−	0.620541i	0.0141514	−	0.0435535i
$204$	1.23607	−	0.898056i	0.0865421	−	0.0628765i
$205$	−5.66312	−	4.11450i	−0.395529	−	0.287369i
$206$	3.11803	+	9.59632i	0.217244	+	0.668607i
$207$	−34.5066	−	25.0705i	−2.39837	−	1.74252i
$208$	4.85410	−	14.9394i	0.336571	−	1.03586i
$209$	−1.38197	+	4.25325i	−0.0955926	+	0.294204i
$210$	−0.381966	−	1.17557i	−0.0263582	−	0.0811221i
$211$	23.1803			1.59580			0.797900	−	0.602790i	$-0.205944\pi$
$211$	23.1803			1.59580			0.797900	+	0.602790i	$0.205944\pi$
$212$	−6.47214			−0.444508
$213$	9.18034	+	28.2542i	0.629027	+	1.93594i
$214$	−7.54508	+	5.48183i	−0.515771	+	0.374730i
$215$	−1.00000	−	0.726543i	−0.0681994	−	0.0495498i
$216$	32.3607			2.20187
$217$		0			0
$218$	−22.5623			−1.52811
$219$	22.1803	+	16.1150i	1.49881	+	1.08895i
$220$	−1.00000	+	0.726543i	−0.0674200	+	0.0489835i
$221$	−0.763932	−	2.35114i	−0.0513876	−	0.158155i
$222$	10.4721			0.702844
$223$	4.00000			0.267860			0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000			0.267860			0.133930	+	0.990991i	$0.457240\pi$
$224$	−0.246711	−	0.759299i	−0.0164841	−	0.0507328i
$225$	−9.23607	+	28.4257i	−0.615738	+	1.89505i
$226$	1.73607	−	5.34307i	0.115482	−	0.355416i
$227$	5.23607	+	3.80423i	0.347530	+	0.252495i	0.747832	−	0.663888i	$-0.231095\pi$
$227$	5.23607	+	3.80423i	0.347530	+	0.252495i	−0.400302	+	0.916383i	$0.631095\pi$
$228$	1.38197	+	4.25325i	0.0915229	+	0.281679i
$229$	10.8541	+	7.88597i	0.717259	+	0.521119i	0.885507	−	0.464625i	$-0.153811\pi$
$229$	10.8541	+	7.88597i	0.717259	+	0.521119i	−0.168248	+	0.985745i	$0.553811\pi$
$230$	−7.47214	+	5.42882i	−0.492698	+	0.357966i
$231$	−0.472136	+	1.45309i	−0.0310643	+	0.0956060i
$232$	5.00000	−	3.63271i	0.328266	−	0.238499i
$233$	−14.5172	+	10.5474i	−0.951055	+	0.690982i	−0.951056	−	0.309018i	$-0.900000\pi$
$233$	−14.5172	+	10.5474i	−0.951055	+	0.690982i	1.33829e−6		1.00000i	$0.500000\pi$
$234$	−12.0902	+	37.2097i	−0.790359	+	2.43248i
$235$	−2.00000	+	1.45309i	−0.130466	+	0.0947888i
$236$	−1.11803	−	0.812299i	−0.0727778	−	0.0528762i
$237$	11.7082	+	36.0341i	0.760530	+	2.34067i
$238$	−0.236068	−	0.171513i	−0.0153020	−	0.0111176i
$239$	−3.61803	+	11.1352i	−0.234031	+	0.720274i	0.763217	+	0.646142i	$0.223619\pi$
$239$	−3.61803	+	11.1352i	−0.234031	+	0.720274i	−0.997248	+	0.0741319i	$0.976381\pi$
$240$	4.85410	−	14.9394i	0.313331	−	0.964333i
$241$	4.43769	+	13.6578i	0.285857	+	0.879777i	0.986140	+	0.165913i	$0.0530569\pi$
$241$	4.43769	+	13.6578i	0.285857	+	0.879777i	−0.700283	+	0.713865i	$0.746943\pi$
$242$	−11.3262			−0.728078
$243$	−35.5967			−2.28353
$244$	1.56231	+	4.80828i	0.100016	+	0.307819i
$245$	5.61803	−	4.08174i	0.358923	−	0.260773i
$246$	29.6525	+	21.5438i	1.89057	+	1.37358i
$247$	7.23607			0.460420
$248$		0			0
$249$	48.3607			3.06473
$250$	11.7812	+	8.55951i	0.745106	+	0.541351i
$251$	1.47214	−	1.06957i	0.0929204	−	0.0675106i	−0.540355	−	0.841437i	$-0.681710\pi$
$251$	1.47214	−	1.06957i	0.0929204	−	0.0675106i	0.633275	+	0.773927i	$0.281710\pi$
$252$	0.336881	+	1.03681i	0.0212215	+	0.0653131i
$253$	11.4164			0.717743
$254$	20.1803			1.26623
$255$	−0.763932	−	2.35114i	−0.0478393	−	0.147234i
$256$	4.19098	−	12.8985i	0.261936	−	0.806157i
$257$	0.600813	−	1.84911i	0.0374777	−	0.115344i	−0.930567	−	0.366121i	$-0.880686\pi$
$257$	0.600813	−	1.84911i	0.0374777	−	0.115344i	0.968045	+	0.250776i	$0.0806858\pi$
$258$	5.23607	+	3.80423i	0.325983	+	0.236841i
$259$	−0.145898	−	0.449028i	−0.00906566	−	0.0279012i
$260$	1.61803	+	1.17557i	0.100346	+	0.0729058i
$261$	−16.7082	+	12.1392i	−1.03421	+	0.751399i
$262$	6.00000	−	18.4661i	0.370681	−	1.14084i
$263$	18.7984	−	13.6578i	1.15916	−	0.842177i	0.169486	−	0.985533i	$-0.445789\pi$
$263$	18.7984	−	13.6578i	1.15916	−	0.842177i	0.989671	+	0.143355i	$0.0457892\pi$
$264$	−11.7082	+	8.50651i	−0.720590	+	0.523539i
$265$	−3.23607	+	9.95959i	−0.198790	+	0.611813i
$266$	0.690983	−	0.502029i	0.0423669	−	0.0307813i
$267$	30.6525	+	22.2703i	1.87590	+	1.36292i
$268$	1.52786	+	4.70228i	0.0933292	+	0.287238i
$269$	8.94427	+	6.49839i	0.545342	+	0.396214i	0.826065	−	0.563575i	$-0.190574\pi$
$269$	8.94427	+	6.49839i	0.545342	+	0.396214i	−0.280723	+	0.959789i	$0.590574\pi$
$270$	−7.23607	+	22.2703i	−0.440373	+	1.35533i
$271$	−4.38197	+	13.4863i	−0.266185	+	0.819235i	0.725232	+	0.688504i	$0.241732\pi$
$271$	−4.38197	+	13.4863i	−0.266185	+	0.819235i	−0.991418	+	0.130731i	$0.958268\pi$
$272$	−1.14590	−	3.52671i	−0.0694803	−	0.213838i
$273$	2.47214			0.149620
$274$	10.1803			0.615017
$275$	−2.47214	−	7.60845i	−0.149075	−	0.458807i
$276$	9.23607	−	6.71040i	0.555946	−	0.403918i
$277$	10.2361	+	7.43694i	0.615026	+	0.446842i	0.851180	−	0.524873i	$-0.175887\pi$
$277$	10.2361	+	7.43694i	0.615026	+	0.446842i	−0.236155	+	0.971715i	$0.575887\pi$
$278$	21.7082			1.30197
$279$		0			0
$280$	−0.527864			−0.0315459
$281$	−13.7533	−	9.99235i	−0.820452	−	0.596094i	0.0963896	−	0.995344i	$-0.469271\pi$
$281$	−13.7533	−	9.99235i	−0.820452	−	0.596094i	−0.916842	+	0.399250i	$0.869271\pi$
$282$	10.4721	−	7.60845i	0.623607	−	0.453077i
$283$	−4.29180	−	13.2088i	−0.255121	−	0.785181i	−0.993806	−	0.111130i	$-0.964553\pi$
$283$	−4.29180	−	13.2088i	−0.255121	−	0.785181i	0.738685	−	0.674051i	$-0.235447\pi$
$284$	−5.67376			−0.336676
$285$	7.23607			0.428628
$286$	−3.23607	−	9.95959i	−0.191353	−	0.588923i
$287$	0.510643	−	1.57160i	0.0301423	−	0.0927685i
$288$	−7.80902	+	24.0337i	−0.460151	+	1.41620i
$289$	13.2812	+	9.64932i	0.781244	+	0.567607i
$290$	1.38197	+	4.25325i	0.0811518	+	0.249760i
$291$	−41.7426	−	30.3278i	−2.44700	−	1.77785i
$292$	−4.23607	+	3.07768i	−0.247897	+	0.180108i
$293$	−0.145898	+	0.449028i	−0.00852345	+	0.0262325i	−0.955228	−	0.295871i	$-0.904390\pi$
$293$	−0.145898	+	0.449028i	−0.00852345	+	0.0262325i	0.946704	+	0.322104i	$0.104390\pi$
$294$	−29.4164	+	21.3723i	−1.71560	+	1.24646i
$295$	−1.80902	+	1.31433i	−0.105325	+	0.0765231i
$296$	1.38197	−	4.25325i	0.0803251	−	0.247215i
$297$	23.4164	−	17.0130i	1.35876	−	0.987195i
$298$	−13.0902	−	9.51057i	−0.758293	−	0.550932i
$299$	−5.70820	−	17.5680i	−0.330114	−	1.01599i
$300$	−6.47214	−	4.70228i	−0.373669	−	0.271486i
$301$	0.0901699	−	0.277515i	0.00519731	−	0.0159957i
$302$	−7.09017	+	21.8213i	−0.407993	+	1.25567i
$303$	3.00000	+	9.23305i	0.172345	+	0.530425i
$304$	10.8541			0.622525
$305$	8.18034			0.468405
$306$	2.85410	+	8.78402i	0.163158	+	0.502149i
$307$	23.2254	−	16.8743i	1.32555	−	0.963065i	0.325700	−	0.945473i	$-0.394400\pi$
$307$	23.2254	−	16.8743i	1.32555	−	0.963065i	0.999845	−	0.0175916i	$-0.00559986\pi$
$308$	−0.236068	−	0.171513i	−0.0134512	−	0.00977288i
$309$	−20.1803			−1.14802
$310$		0			0
$311$	−29.1803			−1.65467			−0.827333	−	0.561712i	$-0.810143\pi$
$311$	−29.1803			−1.65467			−0.827333	+	0.561712i	$0.810143\pi$
$312$	18.9443	+	13.7638i	1.07251	+	0.779223i
$313$	−13.5623	+	9.85359i	−0.766587	+	0.556958i	−0.900924	−	0.433978i	$-0.857110\pi$
$313$	−13.5623	+	9.85359i	−0.766587	+	0.556958i	0.134337	+	0.990936i	$0.457110\pi$
$314$	10.4443	+	32.1442i	0.589404	+	1.81400i
$315$	1.76393			0.0993863
$316$	−7.23607			−0.407061
$317$	1.25329	+	3.85723i	0.0703917	+	0.216643i	0.980064	−	0.198684i	$-0.0636669\pi$
$317$	1.25329	+	3.85723i	0.0703917	+	0.216643i	−0.909672	+	0.415328i	$0.863667\pi$
$318$	16.9443	−	52.1491i	0.950188	−	2.92438i
$319$	1.70820	−	5.25731i	0.0956411	−	0.294353i
$320$	−3.42705	−	2.48990i	−0.191578	−	0.139190i
$321$	−5.76393	−	17.7396i	−0.321711	−	0.990126i
$322$	−1.76393	−	1.28157i	−0.0983001	−	0.0714192i
$323$	1.38197	−	1.00406i	0.0768946	−	0.0558672i
$324$	4.66312	−	14.3516i	0.259062	−	0.797311i
$325$	−10.4721	+	7.60845i	−0.580890	+	0.422041i
$326$	−14.0172	+	10.1841i	−0.776342	+	0.564046i
$327$	13.9443	−	42.9161i	0.771120	−	2.37326i
$328$	12.6631	−	9.20029i	0.699204	−	0.508001i
$329$	−0.472136	−	0.343027i	−0.0260297	−	0.0189117i
$330$	−3.23607	−	9.95959i	−0.178140	−	0.548258i
$331$	−1.61803	−	1.17557i	−0.0889352	−	0.0646152i	0.542429	−	0.840102i	$-0.317505\pi$
$331$	−1.61803	−	1.17557i	−0.0889352	−	0.0646152i	−0.631364	+	0.775486i	$0.717505\pi$
$332$	−2.85410	+	8.78402i	−0.156639	+	0.482086i
$333$	−4.61803	+	14.2128i	−0.253067	+	0.778859i
$334$	−3.23607	−	9.95959i	−0.177070	−	0.544965i
$335$	8.00000			0.437087
$336$	3.70820			0.202299
$337$	−4.56231	−	14.0413i	−0.248525	−	0.764880i	−0.995037	−	0.0995083i	$-0.968273\pi$
$337$	−4.56231	−	14.0413i	−0.248525	−	0.764880i	0.746512	−	0.665372i	$-0.231727\pi$
$338$	3.30902	−	2.40414i	0.179987	−	0.130768i
$339$	9.09017	+	6.60440i	0.493710	+	0.358702i
$340$	0.472136			0.0256052
$341$		0			0
$342$	−27.0344			−1.46186
$343$	2.66312	+	1.93487i	0.143795	+	0.104473i
$344$	2.23607	−	1.62460i	0.120561	−	0.0875925i
$345$	−5.70820	−	17.5680i	−0.307319	−	0.945832i
$346$	4.76393			0.256111
$347$	24.1803			1.29807			0.649034	−	0.760759i	$-0.275173\pi$
$347$	24.1803			1.29807			0.649034	+	0.760759i	$0.275173\pi$
$348$	−1.70820	−	5.25731i	−0.0915693	−	0.281821i
$349$	−2.43769	+	7.50245i	−0.130487	+	0.401597i	−0.994861	−	0.101252i	$-0.967715\pi$
$349$	−2.43769	+	7.50245i	−0.130487	+	0.401597i	0.864374	+	0.502849i	$0.167715\pi$
$350$	−0.472136	+	1.45309i	−0.0252367	+	0.0776707i
$351$	−37.8885	−	27.5276i	−2.02234	−	1.46932i
$352$	−2.09017	−	6.43288i	−0.111406	−	0.342874i
$353$	−6.00000	−	4.35926i	−0.319348	−	0.232020i	0.416549	−	0.909113i	$-0.363239\pi$
$353$	−6.00000	−	4.35926i	−0.319348	−	0.232020i	−0.735897	+	0.677093i	$0.763239\pi$
$354$	9.47214	−	6.88191i	0.503438	−	0.365769i
$355$	−2.83688	+	8.73102i	−0.150566	+	0.463395i
$356$	−5.85410	+	4.25325i	−0.310267	+	0.225422i
$357$	0.472136	−	0.343027i	0.0249881	−	0.0181549i
$358$	0.854102	−	2.62866i	0.0451407	−	0.138929i
$359$	−17.9894	+	13.0700i	−0.949442	+	0.689810i	−0.950675	−	0.310189i	$-0.899608\pi$
$359$	−17.9894	+	13.0700i	−0.949442	+	0.689810i	0.00123287	+	0.999999i	$0.499608\pi$
$360$	13.5172	+	9.82084i	0.712420	+	0.517603i
$361$	−4.32624	−	13.3148i	−0.227697	−	0.700778i
$362$	5.47214	+	3.97574i	0.287609	+	0.208960i
$363$	7.00000	−	21.5438i	0.367405	−	1.13076i
$364$	−0.145898	+	0.449028i	−0.00764713	+	0.0235355i
$365$	2.61803	+	8.05748i	0.137034	+	0.421748i
$366$	−42.8328			−2.23891
$367$	18.0000			0.939592			0.469796	−	0.882775i	$-0.344327\pi$
$367$	18.0000			0.939592			0.469796	+	0.882775i	$0.344327\pi$
$368$	−8.56231	−	26.3521i	−0.446341	−	1.37370i
$369$	−42.3156	+	30.7441i	−2.20286	+	1.60047i
$370$	2.61803	+	1.90211i	0.136105	+	0.0988861i
$371$	−2.47214			−0.128347
$372$		0			0
$373$	19.0000			0.983783			0.491891	−	0.870657i	$-0.336306\pi$
$373$	19.0000			0.983783			0.491891	+	0.870657i	$0.336306\pi$
$374$	−2.00000	−	1.45309i	−0.103418	−	0.0751372i
$375$	−23.5623	+	17.1190i	−1.21675	+	0.884022i
$376$	−1.70820	−	5.25731i	−0.0880939	−	0.271125i
$377$	−8.94427			−0.460653
$378$	−5.52786			−0.284323
$379$	−0.652476	−	2.00811i	−0.0335154	−	0.103150i	0.932899	−	0.360137i	$-0.117270\pi$
$379$	−0.652476	−	2.00811i	−0.0335154	−	0.103150i	−0.966415	+	0.256987i	$0.917270\pi$
$380$	−0.427051	+	1.31433i	−0.0219073	+	0.0674236i
$381$	−12.4721	+	38.3853i	−0.638967	+	1.96654i
$382$	25.1074	+	18.2416i	1.28461	+	0.933321i
$383$	−7.38197	−	22.7194i	−0.377201	−	1.16090i	−0.941982	−	0.335664i	$-0.891039\pi$
$383$	−7.38197	−	22.7194i	−0.377201	−	1.16090i	0.564781	−	0.825241i	$-0.308961\pi$
$384$	35.6525	+	25.9030i	1.81938	+	1.32186i
$385$	−0.381966	+	0.277515i	−0.0194668	+	0.0141435i
$386$	1.73607	−	5.34307i	0.0883635	−	0.271955i
$387$	−7.47214	+	5.42882i	−0.379830	+	0.275963i
$388$	7.97214	−	5.79210i	0.404724	−	0.294049i
$389$	−5.52786	+	17.0130i	−0.280274	+	0.862594i	0.707502	+	0.706712i	$0.249822\pi$
$389$	−5.52786	+	17.0130i	−0.280274	+	0.862594i	−0.987776	+	0.155883i	$0.950178\pi$
$390$	−13.7082	+	9.95959i	−0.694142	+	0.504324i
$391$	−3.52786	−	2.56314i	−0.178412	−	0.129624i
$392$	4.79837	+	14.7679i	0.242354	+	0.745890i
$393$	31.4164	+	22.8254i	1.58475	+	1.15139i
$394$	5.70820	−	17.5680i	0.287575	−	0.885065i
$395$	−3.61803	+	11.1352i	−0.182043	+	0.560271i
$396$	2.85410	+	8.78402i	0.143424	+	0.441414i
$397$	−7.00000			−0.351320			−0.175660	−	0.984451i	$-0.556206\pi$
$397$	−7.00000			−0.351320			−0.175660	+	0.984451i	$0.556206\pi$
$398$	−30.6525			−1.53647
$399$	0.527864	+	1.62460i	0.0264263	+	0.0813317i
$400$	−15.7082	+	11.4127i	−0.785410	+	0.570634i
$401$	−30.8885	−	22.4418i	−1.54250	−	1.12069i	−0.948743	−	0.316048i	$-0.897644\pi$
$401$	−30.8885	−	22.4418i	−1.54250	−	1.12069i	−0.593757	−	0.804644i	$-0.702356\pi$
$402$	−41.8885			−2.08921
$403$		0			0
$404$	−1.85410			−0.0922450
$405$	−19.7533	−	14.3516i	−0.981549	−	0.713137i
$406$	−0.854102	+	0.620541i	−0.0423884	+	0.0307970i
$407$	−1.23607	−	3.80423i	−0.0612696	−	0.188568i
$408$	5.52786			0.273670
$409$	−3.81966			−0.188870			−0.0944350	−	0.995531i	$-0.530104\pi$
$409$	−3.81966			−0.188870			−0.0944350	+	0.995531i	$0.530104\pi$
$410$	3.50000	+	10.7719i	0.172853	+	0.531986i
$411$	−6.29180	+	19.3642i	−0.310351	+	0.955163i
$412$	1.19098	−	3.66547i	0.0586755	−	0.180585i
$413$	−0.427051	−	0.310271i	−0.0210138	−	0.0152674i
$414$	21.3262	+	65.6354i	1.04813	+	3.22580i
$415$	12.0902	+	8.78402i	0.593483	+	0.431191i
$416$	−8.85410	+	6.43288i	−0.434108	+	0.315398i
$417$	−13.4164	+	41.2915i	−0.657004	+	2.02205i
$418$	5.85410	−	4.25325i	0.286333	−	0.208033i
$419$	8.19098	−	5.95110i	0.400156	−	0.290730i	−0.369449	−	0.929251i	$-0.620453\pi$
$419$	8.19098	−	5.95110i	0.400156	−	0.290730i	0.769604	+	0.638521i	$0.220453\pi$
$420$	−0.145898	+	0.449028i	−0.00711910	+	0.0219103i
$421$	−23.7533	+	17.2578i	−1.15766	+	0.841092i	−0.989481	−	0.144663i	$-0.953790\pi$
$421$	−23.7533	+	17.2578i	−1.15766	+	0.841092i	−0.168184	+	0.985756i	$0.553790\pi$
$422$	−30.3435	−	22.0458i	−1.47710	−	1.07317i
$423$	5.70820	+	17.5680i	0.277542	+	0.854188i
$424$	−18.9443	−	13.7638i	−0.920015	−	0.668430i
$425$	−0.944272	+	2.90617i	−0.0458039	+	0.140970i
$426$	14.8541	−	45.7162i	0.719684	−	2.21496i
$427$	0.596748	+	1.83660i	0.0288786	+	0.0888793i
$428$	3.56231			0.172191
$429$	20.9443			1.01120
$430$	0.618034	+	1.90211i	0.0298042	+	0.0917280i
$431$	−9.70820	+	7.05342i	−0.467628	+	0.339751i	−0.796516	−	0.604617i	$-0.793326\pi$
$431$	−9.70820	+	7.05342i	−0.467628	+	0.339751i	0.328888	+	0.944369i	$0.393326\pi$
$432$	−56.8328	−	41.2915i	−2.73437	−	1.98664i
$433$	10.1803			0.489236			0.244618	−	0.969620i	$-0.421337\pi$
$433$	10.1803			0.489236			0.244618	+	0.969620i	$0.421337\pi$
$434$		0			0
$435$	−8.94427			−0.428845
$436$	6.97214	+	5.06555i	0.333905	+	0.242596i
$437$	10.3262	−	7.50245i	0.493971	−	0.358891i
$438$	−13.7082	−	42.1895i	−0.655003	−	2.01589i
$439$	−1.18034			−0.0563345			−0.0281673	−	0.999603i	$-0.508967\pi$
$439$	−1.18034			−0.0563345			−0.0281673	+	0.999603i	$0.508967\pi$
$440$	−4.47214			−0.213201
$441$	−16.0344	−	49.3489i	−0.763545	−	2.34995i
$442$	−1.23607	+	3.80423i	−0.0587938	+	0.180949i
$443$	9.48936	−	29.2052i	0.450853	−	1.38758i	−0.425083	−	0.905155i	$-0.639755\pi$
$443$	9.48936	−	29.2052i	0.450853	−	1.38758i	0.875936	−	0.482428i	$-0.160245\pi$
$444$	−3.23607	−	2.35114i	−0.153577	−	0.111580i
$445$	3.61803	+	11.1352i	0.171511	+	0.527857i
$446$	−5.23607	−	3.80423i	−0.247935	−	0.180135i
$447$	26.1803	−	19.0211i	1.23829	−	0.899669i
$448$	0.309017	−	0.951057i	0.0145997	−	0.0449332i
$449$	25.3262	−	18.4006i	1.19522	−	0.868377i	0.201413	−	0.979506i	$-0.435447\pi$
$449$	25.3262	−	18.4006i	1.19522	−	0.868377i	0.993806	+	0.111129i	$0.0354466\pi$
$450$	39.1246	−	28.4257i	1.84435	−	1.34000i
$451$	4.32624	−	13.3148i	0.203715	−	0.626969i
$452$	−1.73607	+	1.26133i	−0.0816578	+	0.0593278i
$453$	−37.1246	−	26.9726i	−1.74427	−	1.26728i
$454$	−3.23607	−	9.95959i	−0.151876	−	0.467427i
$455$	0.618034	+	0.449028i	0.0289739	+	0.0210508i
$456$	−5.00000	+	15.3884i	−0.234146	+	0.720629i
$457$	−0.944272	+	2.90617i	−0.0441712	+	0.135945i	−0.970710	−	0.240254i	$-0.922769\pi$
$457$	−0.944272	+	2.90617i	−0.0441712	+	0.135945i	0.926539	+	0.376199i	$0.122769\pi$
$458$	−6.70820	−	20.6457i	−0.313454	−	0.964712i
$459$	−11.0557			−0.516037
$460$	3.52786			0.164488
$461$	10.6180	+	32.6789i	0.494531	+	1.52201i	0.817686	+	0.575664i	$0.195256\pi$
$461$	10.6180	+	32.6789i	0.494531	+	1.52201i	−0.323155	+	0.946346i	$0.604744\pi$
$462$	2.00000	−	1.45309i	0.0930484	−	0.0676036i
$463$	2.09017	+	1.51860i	0.0971384	+	0.0705752i	0.635294	−	0.772270i	$-0.280879\pi$
$463$	2.09017	+	1.51860i	0.0971384	+	0.0705752i	−0.538156	+	0.842845i	$0.680879\pi$
$464$	−13.4164			−0.622841
$465$		0			0
$466$	29.0344			1.34499
$467$	−3.80902	−	2.76741i	−0.176260	−	0.128061i	0.496157	−	0.868233i	$-0.334744\pi$
$467$	−3.80902	−	2.76741i	−0.176260	−	0.128061i	−0.672417	+	0.740172i	$0.734744\pi$
$468$	12.0902	−	8.78402i	0.558868	−	0.406042i
$469$	0.583592	+	1.79611i	0.0269478	+	0.0829367i
$470$	4.00000			0.184506
$471$	−67.5967			−3.11469
$472$	−1.54508	−	4.75528i	−0.0711183	−	0.218880i
$473$	0.763932	−	2.35114i	0.0351256	−	0.108106i
$474$	18.9443	−	58.3045i	0.870139	−	2.67801i
$475$	−7.23607	−	5.25731i	−0.332014	−	0.241222i
$476$	0.0344419	+	0.106001i	0.00157864	+	0.00485855i
$477$	63.3050	+	45.9937i	2.89853	+	2.10591i
$478$	15.3262	−	11.1352i	0.701006	−	0.509311i
$479$	7.19756	−	22.1518i	0.328865	−	1.01214i	−0.640801	−	0.767707i	$-0.721398\pi$
$479$	7.19756	−	22.1518i	0.328865	−	1.01214i	0.969666	−	0.244435i	$-0.0786025\pi$
$480$	−8.85410	+	6.43288i	−0.404133	+	0.293620i
$481$	−5.23607	+	3.80423i	−0.238744	+	0.173458i
$482$	7.18034	−	22.0988i	0.327056	−	1.00657i
$483$	3.52786	−	2.56314i	0.160523	−	0.116627i
$484$	3.50000	+	2.54290i	0.159091	+	0.115586i
$485$	−4.92705	−	15.1639i	−0.223726	−	0.688557i
$486$	46.5967	+	33.8545i	2.11367	+	1.53567i
$487$	−5.94427	+	18.2946i	−0.269361	+	0.829007i	0.721296	+	0.692627i	$0.243547\pi$
$487$	−5.94427	+	18.2946i	−0.269361	+	0.829007i	−0.990657	+	0.136380i	$0.956453\pi$
$488$	−5.65248	+	17.3965i	−0.255876	+	0.787504i
$489$	−10.7082	−	32.9565i	−0.484242	−	1.49034i
$490$	−11.2361			−0.507594
$491$	4.36068			0.196795			0.0983974	−	0.995147i	$-0.468628\pi$
$491$	4.36068			0.196795			0.0983974	+	0.995147i	$0.468628\pi$
$492$	−4.32624	−	13.3148i	−0.195042	−	0.600277i
$493$	−1.70820	+	1.24108i	−0.0769336	+	0.0558956i
$494$	−9.47214	−	6.88191i	−0.426172	−	0.309632i
$495$	14.9443			0.671695
$496$		0			0
$497$	−2.16718			−0.0972115
$498$	−63.3050	−	45.9937i	−2.83676	−	2.06103i
$499$	5.32624	−	3.86974i	0.238435	−	0.173233i	−0.462151	−	0.886801i	$-0.652922\pi$
$499$	5.32624	−	3.86974i	0.238435	−	0.173233i	0.700586	+	0.713568i	$0.252922\pi$
$500$	−1.71885	−	5.29007i	−0.0768692	−	0.236579i
$501$	20.9443			0.935721
$502$	−2.94427			−0.131409
$503$	9.16312	+	28.2012i	0.408563	+	1.25743i	0.917883	+	0.396851i	$0.129897\pi$
$503$	9.16312	+	28.2012i	0.408563	+	1.25743i	−0.509320	+	0.860577i	$0.670103\pi$
$504$	−1.21885	+	3.75123i	−0.0542918	+	0.167093i
$505$	−0.927051	+	2.85317i	−0.0412532	+	0.126964i
$506$	−14.9443	−	10.8576i	−0.664354	−	0.482681i
$507$	2.52786	+	7.77997i	0.112266	+	0.345520i
$508$	−6.23607	−	4.53077i	−0.276681	−	0.201020i
$509$	−23.9443	+	17.3965i	−1.06131	+	0.771088i	−0.974331	−	0.225122i	$-0.927722\pi$
$509$	−23.9443	+	17.3965i	−1.06131	+	0.771088i	−0.0869807	+	0.996210i	$0.527722\pi$
$510$	−1.23607	+	3.80423i	−0.0547340	+	0.168454i
$511$	−1.61803	+	1.17557i	−0.0715776	+	0.0520042i
$512$	4.28115	−	3.11044i	0.189202	−	0.137463i
$513$	10.0000	−	30.7768i	0.441511	−	1.35883i
$514$	−2.54508	+	1.84911i	−0.112259	+	0.0815609i
$515$	−5.04508	−	3.66547i	−0.222313	−	0.161520i
$516$	−0.763932	−	2.35114i	−0.0336302	−	0.103503i
$517$	−4.00000	−	2.90617i	−0.175920	−	0.127813i
$518$	−0.236068	+	0.726543i	−0.0103722	+	0.0319224i
$519$	−2.94427	+	9.06154i	−0.129239	+	0.397757i
$520$	2.23607	+	6.88191i	0.0980581	+	0.301792i
$521$	2.00000			0.0876216			0.0438108	−	0.999040i	$-0.486050\pi$
$521$	2.00000			0.0876216			0.0438108	+	0.999040i	$0.486050\pi$
$522$	33.4164			1.46260
$523$	−5.47214	−	16.8415i	−0.239280	−	0.736427i	−0.996525	−	0.0832966i	$-0.973455\pi$
$523$	−5.47214	−	16.8415i	−0.239280	−	0.736427i	0.757245	−	0.653131i	$-0.226545\pi$
$524$	−6.00000	+	4.35926i	−0.262111	+	0.190435i
$525$	−2.47214	−	1.79611i	−0.107893	−	0.0783888i
$526$	−37.5967			−1.63930
$527$		0			0
$528$	31.4164			1.36722
$529$	−7.75329	−	5.63309i	−0.337100	−	0.244917i
$530$	13.7082	−	9.95959i	0.595446	−	0.432617i
$531$	5.16312	+	15.8904i	0.224060	+	0.689587i
$532$	−0.326238			−0.0141442
$533$	−22.6525			−0.981188
$534$	−18.9443	−	58.3045i	−0.819799	−	2.52308i
$535$	1.78115	−	5.48183i	0.0770060	−	0.237000i
$536$	−5.52786	+	17.0130i	−0.238767	+	0.734850i
$537$	4.47214	+	3.24920i	0.192987	+	0.140213i
$538$	−5.52786	−	17.0130i	−0.238323	−	0.733483i
$539$	11.2361	+	8.16348i	0.483972	+	0.351626i
$540$	7.23607	−	5.25731i	0.311391	−	0.226239i
$541$	−7.83688	+	24.1194i	−0.336934	+	1.03698i	0.628828	+	0.777545i	$0.283535\pi$
$541$	−7.83688	+	24.1194i	−0.336934	+	1.03698i	−0.965762	+	0.259431i	$0.916465\pi$
$542$	18.5623	−	13.4863i	0.797319	−	0.579286i
$543$	−10.9443	+	7.95148i	−0.469664	+	0.341231i
$544$	−0.798374	+	2.45714i	−0.0342300	+	0.105349i
$545$	11.2812	−	8.19624i	0.483231	−	0.351088i
$546$	−3.23607	−	2.35114i	−0.138491	−	0.100620i
$547$	−3.74671	−	11.5312i	−0.160198	−	0.493038i	0.838453	−	0.544975i	$-0.183461\pi$
$547$	−3.74671	−	11.5312i	−0.160198	−	0.493038i	−0.998650	+	0.0519364i	$0.983461\pi$
$548$	−3.14590	−	2.28563i	−0.134386	−	0.0976372i
$549$	18.8885	−	58.1330i	0.806143	−	2.48105i
$550$	−4.00000	+	12.3107i	−0.170561	+	0.524931i
$551$	−1.90983	−	5.87785i	−0.0813615	−	0.250405i
$552$	41.3050			1.75806
$553$	−2.76393			−0.117534
$554$	−6.32624	−	19.4702i	−0.268776	−	0.827208i
$555$	−5.23607	+	3.80423i	−0.222259	+	0.161480i
$556$	−6.70820	−	4.87380i	−0.284491	−	0.206695i
$557$	−12.0000			−0.508456			−0.254228	−	0.967144i	$-0.581821\pi$
$557$	−12.0000			−0.508456			−0.254228	+	0.967144i	$0.581821\pi$
$558$		0			0
$559$	−4.00000			−0.169182
$560$	0.927051	+	0.673542i	0.0391751	+	0.0284623i
$561$	4.00000	−	2.90617i	0.168880	−	0.122699i
$562$	8.50000	+	26.1603i	0.358551	+	1.10351i
$563$	27.5410			1.16072			0.580358	−	0.814362i	$-0.302913\pi$
$563$	27.5410			1.16072			0.580358	+	0.814362i	$0.302913\pi$
$564$	−4.94427			−0.208191
$565$	1.07295	+	3.30220i	0.0451393	+	0.138924i
$566$	−6.94427	+	21.3723i	−0.291890	+	0.898344i
$567$	1.78115	−	5.48183i	0.0748014	−	0.230215i
$568$	−16.6074	−	12.0660i	−0.696831	−	0.506277i
$569$	1.70820	+	5.25731i	0.0716116	+	0.220398i	0.980456	−	0.196737i	$-0.0630344\pi$
$569$	1.70820	+	5.25731i	0.0716116	+	0.220398i	−0.908845	+	0.417135i	$0.863034\pi$
$570$	−9.47214	−	6.88191i	−0.396744	−	0.288251i
$571$	−22.7984	+	16.5640i	−0.954082	+	0.693181i	−0.951769	−	0.306816i	$-0.900736\pi$
$571$	−22.7984	+	16.5640i	−0.954082	+	0.693181i	−0.00231340	+	0.999997i	$0.500736\pi$
$572$	−1.23607	+	3.80423i	−0.0516826	+	0.159063i
$573$	−50.2148	+	36.4832i	−2.09775	+	1.52411i
$574$	−2.16312	+	1.57160i	−0.0902868	+	0.0655972i
$575$	−7.05573	+	21.7153i	−0.294244	+	0.905591i
$576$	−25.6074	+	18.6049i	−1.06697	+	0.775202i
$577$	23.3262	+	16.9475i	0.971084	+	0.705534i	0.955698	−	0.294348i	$-0.0951024\pi$
$577$	23.3262	+	16.9475i	0.971084	+	0.705534i	0.0153856	+	0.999882i	$0.495102\pi$
$578$	−8.20820	−	25.2623i	−0.341416	−	1.05077i
$579$	9.09017	+	6.60440i	0.377775	+	0.274469i
$580$	0.527864	−	1.62460i	0.0219184	−	0.0674578i
$581$	−1.09017	+	3.35520i	−0.0452279	+	0.139197i
$582$	25.7984	+	79.3992i	1.06938	+	3.29120i
$583$	−20.9443			−0.867423
$584$	−18.9443			−0.783920
$585$	−7.47214	−	22.9969i	−0.308935	−	0.950804i
$586$	0.618034	−	0.449028i	0.0255307	−	0.0185492i
$587$	5.23607	+	3.80423i	0.216116	+	0.157017i	0.690576	−	0.723259i	$-0.257357\pi$
$587$	5.23607	+	3.80423i	0.216116	+	0.157017i	−0.474461	+	0.880277i	$0.657357\pi$
$588$	13.8885			0.572754
$589$		0			0
$590$	3.61803			0.148952
$591$	29.8885	+	21.7153i	1.22945	+	0.893248i
$592$	−7.85410	+	5.70634i	−0.322802	+	0.234529i
$593$	−2.01722	−	6.20837i	−0.0828373	−	0.254947i	0.901056	−	0.433702i	$-0.142793\pi$
$593$	−2.01722	−	6.20837i	−0.0828373	−	0.254947i	−0.983894	+	0.178755i	$0.942793\pi$
$594$	−46.8328			−1.92157
$595$	0.180340			0.00739321
$596$	1.90983	+	5.87785i	0.0782297	+	0.240766i
$597$	18.9443	−	58.3045i	0.775337	−	2.38624i
$598$	−9.23607	+	28.4257i	−0.377691	+	1.16241i
$599$	11.8090	+	8.57975i	0.482503	+	0.350559i	0.802294	−	0.596929i	$-0.203613\pi$
$599$	11.8090	+	8.57975i	0.482503	+	0.350559i	−0.319791	+	0.947488i	$0.603613\pi$
$600$	−8.94427	−	27.5276i	−0.365148	−	1.12381i
$601$	−24.7082	−	17.9516i	−1.00787	−	0.732259i	−0.0441077	−	0.999027i	$-0.514044\pi$
$601$	−24.7082	−	17.9516i	−1.00787	−	0.732259i	−0.963761	+	0.266767i	$0.914044\pi$
$602$	−0.381966	+	0.277515i	−0.0155678	+	0.0113106i
$603$	18.4721	−	56.8514i	0.752244	−	2.31517i
$604$	7.09017	−	5.15131i	0.288495	−	0.209604i
$605$	5.66312	−	4.11450i	0.230239	−	0.167278i
$606$	4.85410	−	14.9394i	0.197184	−	0.606871i
$607$	−18.1803	+	13.2088i	−0.737917	+	0.536128i	−0.892058	−	0.451921i	$-0.850739\pi$
$607$	−18.1803	+	13.2088i	−0.737917	+	0.536128i	0.154141	+	0.988049i	$0.450739\pi$
$608$	−6.11803	−	4.44501i	−0.248119	−	0.180269i
$609$	−0.652476	−	2.00811i	−0.0264397	−	0.0813729i
$610$	−10.7082	−	7.77997i	−0.433563	−	0.315002i
$611$	−2.47214	+	7.60845i	−0.100012	+	0.307805i
$612$	1.09017	−	3.35520i	0.0440675	−	0.135626i
$613$	−13.5623	−	41.7405i	−0.547776	−	1.68588i	−0.714296	−	0.699844i	$-0.753253\pi$
$613$	−13.5623	−	41.7405i	−0.547776	−	1.68588i	0.166519	−	0.986038i	$-0.446747\pi$
$614$	−46.4508			−1.87460
$615$	−22.6525			−0.913436
$616$	−0.326238	−	1.00406i	−0.0131445	−	0.0404546i
$617$	−26.2705	+	19.0866i	−1.05761	+	0.768399i	−0.973645	−	0.228069i	$-0.926759\pi$
$617$	−26.2705	+	19.0866i	−1.05761	+	0.768399i	−0.0839660	+	0.996469i	$0.526759\pi$
$618$	26.4164	+	19.1926i	1.06262	+	0.772041i
$619$	6.18034			0.248409			0.124204	−	0.992257i	$-0.460362\pi$
$619$	6.18034			0.248409			0.124204	+	0.992257i	$0.460362\pi$
$620$		0			0
$621$	−82.6099			−3.31502
$622$	38.1976	+	27.7522i	1.53158	+	1.11276i
$623$	−2.23607	+	1.62460i	−0.0895862	+	0.0650882i
$624$	−15.7082	−	48.3449i	−0.628831	−	1.93534i
$625$	11.0000			0.440000
$626$	27.1246			1.08412
$627$	4.47214	+	13.7638i	0.178600	+	0.549674i
$628$	3.98936	−	12.2780i	0.159193	−	0.489945i
$629$	−0.472136	+	1.45309i	−0.0188253	+	0.0579383i
$630$	−2.30902	−	1.67760i	−0.0919934	−	0.0668371i
$631$	10.6180	+	32.6789i	0.422697	+	1.30093i	0.905182	+	0.425024i	$0.139734\pi$
$631$	10.6180	+	32.6789i	0.422697	+	1.30093i	−0.482485	+	0.875904i	$0.660266\pi$
$632$	−21.1803	−	15.3884i	−0.842509	−	0.612118i
$633$	60.6869	−	44.0916i	2.41209	−	1.75248i
$634$	2.02786	−	6.24112i	0.0805368	−	0.247867i
$635$	−10.0902	+	7.33094i	−0.400416	+	0.290919i
$636$	−16.9443	+	12.3107i	−0.671884	+	0.488152i
$637$	6.94427	−	21.3723i	0.275142	−	0.846800i
$638$	−7.23607	+	5.25731i	−0.286479	+	0.208139i
$639$	55.4959	+	40.3202i	2.19539	+	1.59504i
$640$	4.20820	+	12.9515i	0.166344	+	0.511954i
$641$	−9.70820	−	7.05342i	−0.383451	−	0.278593i	0.379316	−	0.925267i	$-0.376159\pi$
$641$	−9.70820	−	7.05342i	−0.383451	−	0.278593i	−0.762767	+	0.646674i	$0.776159\pi$
$642$	−9.32624	+	28.7032i	−0.368077	+	1.13283i
$643$	6.03444	−	18.5721i	0.237975	−	0.732412i	−0.758738	−	0.651396i	$-0.774184\pi$
$643$	6.03444	−	18.5721i	0.237975	−	0.732412i	0.996713	−	0.0810159i	$-0.0258165\pi$
$644$	0.257354	+	0.792055i	0.0101412	+	0.0312113i
$645$	−4.00000			−0.157500
$646$	−2.76393			−0.108745
$647$	−0.291796	−	0.898056i	−0.0114717	−	0.0353062i	0.945157	−	0.326617i	$-0.105909\pi$
$647$	−0.291796	−	0.898056i	−0.0114717	−	0.0353062i	−0.956629	+	0.291311i	$0.905909\pi$
$648$	44.1697	−	32.0912i	1.73515	−	1.26066i
$649$	−3.61803	−	2.62866i	−0.142020	−	0.103184i
$650$	20.9443			0.821502
$651$		0			0
$652$	6.61803			0.259182
$653$	38.2705	+	27.8052i	1.49764	+	1.08810i	0.971309	+	0.237820i	$0.0764329\pi$
$653$	38.2705	+	27.8052i	1.49764	+	1.08810i	0.526332	+	0.850279i	$0.323567\pi$
$654$	−59.0689	+	42.9161i	−2.30978	+	1.67815i
$655$	3.70820	+	11.4127i	0.144892	+	0.445930i
$656$	−33.9787			−1.32665
$657$	63.3050			2.46976
$658$	0.291796	+	0.898056i	0.0113754	+	0.0350099i
$659$	7.92705	−	24.3970i	0.308794	−	0.950370i	−0.669440	−	0.742866i	$-0.733466\pi$
$659$	7.92705	−	24.3970i	0.308794	−	0.950370i	0.978234	−	0.207504i	$-0.0665341\pi$
$660$	−1.23607	+	3.80423i	−0.0481139	+	0.148079i
$661$	0.517221	+	0.375783i	0.0201176	+	0.0146163i	0.597799	−	0.801646i	$-0.296042\pi$
$661$	0.517221	+	0.375783i	0.0201176	+	0.0146163i	−0.577681	+	0.816263i	$0.696042\pi$
$662$	1.00000	+	3.07768i	0.0388661	+	0.119618i
$663$	−6.47214	−	4.70228i	−0.251357	−	0.182622i
$664$	−27.0344	+	19.6417i	−1.04914	+	0.762245i
$665$	−0.163119	+	0.502029i	−0.00632548	+	0.0194678i
$666$	19.5623	−	14.2128i	0.758024	−	0.550737i
$667$	−12.7639	+	9.27354i	−0.494221	+	0.359073i
$668$	−1.23607	+	3.80423i	−0.0478249	+	0.147190i
$669$	10.4721	−	7.60845i	0.404876	−	0.294160i
$670$	−10.4721	−	7.60845i	−0.404574	−	0.293940i
$671$	5.05573	+	15.5599i	0.195174	+	0.600684i
$672$	−2.09017	−	1.51860i	−0.0806301	−	0.0585812i
$673$	−8.96556	+	27.5932i	−0.345597	+	1.06364i	0.615667	+	0.788007i	$0.288887\pi$
$673$	−8.96556	+	27.5932i	−0.345597	+	1.06364i	−0.961263	+	0.275631i	$0.911113\pi$
$674$	−7.38197	+	22.7194i	−0.284343	+	0.875117i
$675$	17.8885	+	55.0553i	0.688530	+	2.11908i
$676$	−1.56231			−0.0600887
$677$	−46.7214			−1.79565			−0.897824	−	0.440355i	$-0.854853\pi$
$677$	−46.7214			−1.79565			−0.897824	+	0.440355i	$0.854853\pi$
$678$	−5.61803	−	17.2905i	−0.215759	−	0.664039i
$679$	3.04508	−	2.21238i	0.116860	−	0.0849035i
$680$	1.38197	+	1.00406i	0.0529960	+	0.0385038i
$681$	20.9443			0.802586
$682$		0			0
$683$	5.18034			0.198220			0.0991101	−	0.995076i	$-0.468400\pi$
$683$	5.18034			0.198220			0.0991101	+	0.995076i	$0.468400\pi$
$684$	8.35410	+	6.06961i	0.319427	+	0.232077i
$685$	−5.09017	+	3.69822i	−0.194485	+	0.141302i
$686$	−1.64590	−	5.06555i	−0.0628407	−	0.193404i
$687$	43.4164			1.65644
$688$	−6.00000			−0.228748
$689$	10.4721	+	32.2299i	0.398957	+	1.22786i
$690$	−9.23607	+	28.4257i	−0.351611	+	1.08215i
$691$	0.982779	−	3.02468i	0.0373867	−	0.115064i	−0.930621	−	0.365983i	$-0.880733\pi$
$691$	0.982779	−	3.02468i	0.0373867	−	0.115064i	0.968008	+	0.250919i	$0.0807327\pi$
$692$	−1.47214	−	1.06957i	−0.0559622	−	0.0406589i
$693$	1.09017	+	3.35520i	0.0414121	+	0.127453i
$694$	−31.6525	−	22.9969i	−1.20151	−	0.872949i
$695$	−10.8541	+	7.88597i	−0.411720	+	0.299132i
$696$	6.18034	−	19.0211i	0.234265	−	0.720994i
$697$	−4.32624	+	3.14320i	−0.163868	+	0.119057i
$698$	10.3262	−	7.50245i	0.390854	−	0.283972i
$699$	−17.9443	+	55.2268i	−0.678715	+	2.08887i
$700$	0.472136	−	0.343027i	0.0178451	−	0.0129652i
$701$	−5.66312	−	4.11450i	−0.213893	−	0.155402i	0.475680	−	0.879618i	$-0.342202\pi$
$701$	−5.66312	−	4.11450i	−0.213893	−	0.155402i	−0.689573	+	0.724216i	$0.742202\pi$
$702$	23.4164	+	72.0683i	0.883795	+	2.72004i
$703$	−3.61803	−	2.62866i	−0.136457	−	0.0991416i
$704$	2.61803	−	8.05748i	0.0986709	−	0.303678i
$705$	−2.47214	+	7.60845i	−0.0931060	+	0.286551i
$706$	3.70820	+	11.4127i	0.139560	+	0.429522i
$707$	−0.708204			−0.0266348
$708$	−4.47214			−0.168073
$709$	7.88854	+	24.2784i	0.296260	+	0.911796i	0.982795	+	0.184699i	$0.0591310\pi$
$709$	7.88854	+	24.2784i	0.296260	+	0.911796i	−0.686535	+	0.727097i	$0.740869\pi$
$710$	12.0172	−	8.73102i	0.450998	−	0.327669i
$711$	70.7771	+	51.4226i	2.65435	+	1.92850i
$712$	−26.1803			−0.981150
$713$		0			0
$714$	−0.944272			−0.0353385
$715$	5.23607	+	3.80423i	0.195818	+	0.142270i
$716$	−0.854102	+	0.620541i	−0.0319193	+	0.0231907i
$717$	11.7082	+	36.0341i	0.437251	+	1.34572i
$718$	35.9787			1.34271
$719$	−13.8197			−0.515386			−0.257693	−	0.966227i	$-0.582962\pi$
$719$	−13.8197			−0.515386			−0.257693	+	0.966227i	$0.582962\pi$
$720$	−11.2082	−	34.4953i	−0.417705	−	1.28556i
$721$	0.454915	−	1.40008i	0.0169419	−	0.0521419i
$722$	−7.00000	+	21.5438i	−0.260513	+	0.801777i
$723$	37.5967	+	27.3156i	1.39824	+	1.01588i
$724$	−0.798374	−	2.45714i	−0.0296713	−	0.0913190i
$725$	8.94427	+	6.49839i	0.332182	+	0.241344i
$726$	−29.6525	+	21.5438i	−1.10051	+	0.799565i
$727$	−13.6697	+	42.0710i	−0.506981	+	1.56033i	0.290434	+	0.956895i	$0.406200\pi$
$727$	−13.6697	+	42.0710i	−0.506981	+	1.56033i	−0.797415	+	0.603432i	$0.793800\pi$
$728$	−1.38197	+	1.00406i	−0.0512191	+	0.0372128i
$729$	−33.9336	+	24.6542i	−1.25680	+	0.913119i
$730$	4.23607	−	13.0373i	0.156784	−	0.482531i
$731$	−0.763932	+	0.555029i	−0.0282550	+	0.0205285i
$732$	13.2361	+	9.61657i	0.489219	+	0.355439i
$733$	1.07295	+	3.30220i	0.0396303	+	0.121969i	0.968914	−	0.247396i	$-0.0795750\pi$
$733$	1.07295	+	3.30220i	0.0396303	+	0.121969i	−0.929284	+	0.369366i	$0.879575\pi$
$734$	−23.5623	−	17.1190i	−0.869701	−	0.631874i
$735$	6.94427	−	21.3723i	0.256143	−	0.788328i
$736$	−5.96556	+	18.3601i	−0.219893	+	0.676762i
$737$	4.94427	+	15.2169i	0.182125	+	0.560522i
$738$	84.6312			3.11532
$739$	6.18034			0.227347			0.113674	−	0.993518i	$-0.463738\pi$
$739$	6.18034			0.227347			0.113674	+	0.993518i	$0.463738\pi$
$740$	−0.381966	−	1.17557i	−0.0140413	−	0.0432148i
$741$	18.9443	−	13.7638i	0.695935	−	0.505627i
$742$	3.23607	+	2.35114i	0.118800	+	0.0863131i
$743$	50.1803			1.84094			0.920469	−	0.390815i	$-0.127807\pi$
$743$	50.1803			1.84094			0.920469	+	0.390815i	$0.127807\pi$
$744$		0			0
$745$	10.0000			0.366372
$746$	−24.8713	−	18.0701i	−0.910604	−	0.661592i
$747$	90.3394	−	65.6354i	3.30535	−	2.40147i
$748$	0.291796	+	0.898056i	0.0106691	+	0.0328362i
$749$	1.36068			0.0497182
$750$	47.1246			1.72075
$751$	−6.65654	−	20.4867i	−0.242901	−	0.747571i	−0.995975	−	0.0896355i	$-0.971430\pi$
$751$	−6.65654	−	20.4867i	−0.242901	−	0.747571i	0.753074	−	0.657936i	$-0.228570\pi$
$752$	−3.70820	+	11.4127i	−0.135224	+	0.416178i
$753$	1.81966	−	5.60034i	0.0663121	−	0.204088i
$754$	11.7082	+	8.50651i	0.426388	+	0.309789i
$755$	−4.38197	−	13.4863i	−0.159476	−	0.490817i
$756$	1.70820	+	1.24108i	0.0621268	+	0.0451377i
$757$	−7.00000	+	5.08580i	−0.254419	+	0.184846i	−0.707683	−	0.706530i	$-0.750260\pi$
$757$	−7.00000	+	5.08580i	−0.254419	+	0.184846i	0.453264	+	0.891376i	$0.350260\pi$
$758$	−1.05573	+	3.24920i	−0.0383458	+	0.118016i
$759$	29.8885	−	21.7153i	1.08489	−	0.788215i
$760$	−4.04508	+	2.93893i	−0.146731	+	0.106606i
$761$	0.618034	−	1.90211i	0.0224037	−	0.0689515i	−0.939230	−	0.343290i	$-0.888459\pi$
$761$	0.618034	−	1.90211i	0.0224037	−	0.0689515i	0.961633	+	0.274338i	$0.0884587\pi$
$762$	52.8328	−	38.3853i	1.91393	−	1.39055i
$763$	2.66312	+	1.93487i	0.0964114	+	0.0700470i
$764$	−3.66312	−	11.2739i	−0.132527	−	0.407876i
$765$	−4.61803	−	3.35520i	−0.166965	−	0.121307i
$766$	−11.9443	+	36.7607i	−0.431564	+	1.32822i
$767$	−2.23607	+	6.88191i	−0.0807397	+	0.248491i
$768$	−13.5623	−	41.7405i	−0.489388	−	1.50618i
$769$	−47.3607			−1.70787			−0.853935	−	0.520380i	$-0.825790\pi$
$769$	−47.3607			−1.70787			−0.853935	+	0.520380i	$0.825790\pi$
$770$	0.763932			0.0275302
$771$	−1.94427	−	5.98385i	−0.0700212	−	0.215503i
$772$	−1.73607	+	1.26133i	−0.0624825	+	0.0453962i
$773$	9.00000	+	6.53888i	0.323708	+	0.235187i	0.737756	−	0.675068i	$-0.235886\pi$
$773$	9.00000	+	6.53888i	0.323708	+	0.235187i	−0.414048	+	0.910255i	$0.635886\pi$
$774$	14.9443			0.537161
$775$		0			0
$776$	35.6525			1.27985
$777$	−1.23607	−	0.898056i	−0.0443437	−	0.0322176i
$778$	23.4164	−	17.0130i	0.839519	−	0.609946i
$779$	−4.83688	−	14.8864i	−0.173299	−	0.533360i
$780$	6.47214			0.231740
$781$	−18.3607			−0.656997
$782$	2.18034	+	6.71040i	0.0779688	+	0.239963i
$783$	−12.3607	+	38.0423i	−0.441735	+	1.35952i
$784$	10.4164	−	32.0584i	0.372015	−	1.14494i
$785$	−16.8992	−	12.2780i	−0.603158	−	0.438220i
$786$	−19.4164	−	59.7576i	−0.692560	−	2.13148i
$787$	−5.94427	−	4.31877i	−0.211890	−	0.153947i	0.476778	−	0.879024i	$-0.341804\pi$
$787$	−5.94427	−	4.31877i	−0.211890	−	0.153947i	−0.688669	+	0.725076i	$0.741804\pi$
$788$	−5.70820	+	4.14725i	−0.203346	+	0.147740i
$789$	23.2361	−	71.5133i	0.827226	−	2.54594i
$790$	15.3262	−	11.1352i	0.545283	−	0.396171i
$791$	−0.663119	+	0.481784i	−0.0235778	+	0.0171303i
$792$	−10.3262	+	31.7809i	−0.366927	+	1.12928i
$793$	21.4164	−	15.5599i	0.760519	−	0.552549i
$794$	9.16312	+	6.65740i	0.325187	+	0.236262i
$795$	10.4721	+	32.2299i	0.371408	+	1.14308i
$796$	9.47214	+	6.88191i	0.335731	+	0.243923i
$797$	−17.1246	+	52.7041i	−0.606585	+	1.86688i	−0.121079	+	0.992643i	$0.538635\pi$
$797$	−17.1246	+	52.7041i	−0.606585	+	1.86688i	−0.485506	+	0.874233i	$0.661365\pi$
$798$	0.854102	−	2.62866i	0.0302349	−	0.0930534i
$799$	0.583592	+	1.79611i	0.0206460	+	0.0635419i
$800$	13.5279			0.478282
$801$	87.4853			3.09114
$802$	19.0902	+	58.7535i	0.674097	+	2.07466i
$803$	−13.7082	+	9.95959i	−0.483752	+	0.351466i
$804$	12.9443	+	9.40456i	0.456509	+	0.331673i
$805$	1.34752			0.0474940
$806$		0			0
$807$	35.7771			1.25941
$808$	−5.42705	−	3.94298i	−0.190923	−	0.138714i
$809$	−18.9443	+	13.7638i	−0.666045	+	0.483910i	−0.868699	−	0.495340i	$-0.835043\pi$
$809$	−18.9443	+	13.7638i	−0.666045	+	0.483910i	0.202654	+	0.979250i	$0.435043\pi$
$810$	12.2082	+	37.5730i	0.428953	+	1.32018i
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$	0.403252			0.0141514
$813$	14.1803	+	43.6426i	0.497326	+	1.53061i
$814$	−2.00000	+	6.15537i	−0.0701000	+	0.215746i
$815$	3.30902	−	10.1841i	0.115910	−	0.356734i
$816$	−9.70820	−	7.05342i	−0.339855	−	0.246919i
$817$	−0.854102	−	2.62866i	−0.0298812	−	0.0919650i
$818$	5.00000	+	3.63271i	0.174821	+	0.127015i
$819$	4.61803	−	3.35520i	0.161367	−	0.117240i
$820$	1.33688	−	4.11450i	0.0466859	−	0.143684i
$821$	−24.7082	+	17.9516i	−0.862322	+	0.626514i	−0.928516	−	0.371293i	$-0.878915\pi$
$821$	−24.7082	+	17.9516i	−0.862322	+	0.626514i	0.0661935	+	0.997807i	$0.478915\pi$
$822$	26.6525	−	19.3642i	0.929612	−	0.675403i
$823$	−4.41641	+	13.5923i	−0.153946	+	0.473798i	−0.998053	−	0.0623779i	$-0.980132\pi$
$823$	−4.41641	+	13.5923i	−0.153946	+	0.473798i	0.844106	+	0.536176i	$0.180132\pi$
$824$	11.2812	−	8.19624i	0.392998	−	0.285529i
$825$	−20.9443	−	15.2169i	−0.729186	−	0.529785i
$826$	0.263932	+	0.812299i	0.00918337	+	0.0282635i
$827$	−14.0344	−	10.1966i	−0.488025	−	0.354571i	0.316399	−	0.948626i	$-0.397526\pi$
$827$	−14.0344	−	10.1966i	−0.488025	−	0.354571i	−0.804424	+	0.594055i	$0.797526\pi$
$828$	8.14590	−	25.0705i	0.283090	−	0.871260i
$829$	5.20163	−	16.0090i	0.180660	−	0.556014i	−0.819187	−	0.573527i	$-0.805575\pi$
$829$	5.20163	−	16.0090i	0.180660	−	0.556014i	0.999847	+	0.0175128i	$0.00557479\pi$
$830$	−7.47214	−	22.9969i	−0.259362	−	0.798233i
$831$	40.9443			1.42034
$832$	−13.7082			−0.475246
$833$	−1.63932	−	5.04531i	−0.0567991	−	0.174810i
$834$	56.8328	−	41.2915i	1.96796	−	1.42981i
$835$	5.23607	+	3.80423i	0.181202	+	0.131651i
$836$	−2.76393			−0.0955926
$837$		0			0
$838$	−16.3820			−0.565906
$839$	−23.4164	−	17.0130i	−0.808424	−	0.587355i	0.104949	−	0.994478i	$-0.466532\pi$
$839$	−23.4164	−	17.0130i	−0.808424	−	0.587355i	−0.913373	+	0.407123i	$0.866532\pi$
$840$	−1.38197	+	1.00406i	−0.0476824	+	0.0346433i
$841$	−6.60081	−	20.3152i	−0.227614	−	0.700525i
$842$	47.5066			1.63718
$843$	−55.0132			−1.89475
$844$	4.42705	+	13.6251i	0.152385	+	0.468994i
$845$	−0.781153	+	2.40414i	−0.0268725	+	0.0827050i
$846$	9.23607	−	28.4257i	0.317543	−	0.977296i
$847$	1.33688	+	0.971301i	0.0459358	+	0.0333743i
$848$	15.7082	+	48.3449i	0.539422	+	1.66017i
$849$	−36.3607	−	26.4176i	−1.24790	−	0.906649i
$850$	4.00000	−	2.90617i	0.137199	−	0.0996808i
$851$	−3.52786	+	10.8576i	−0.120934	+	0.372195i
$852$	−14.8541	+	10.7921i	−0.508893	+	0.369733i
$853$	−8.56231	+	6.22088i	−0.293168	+	0.212999i	−0.724640	−	0.689127i	$-0.757994\pi$
$853$	−8.56231	+	6.22088i	−0.293168	+	0.212999i	0.431473	+	0.902126i	$0.357994\pi$
$854$	0.965558	−	2.97168i	0.0330407	−	0.101689i
$855$	13.5172	−	9.82084i	0.462279	−	0.335865i
$856$	10.4271	+	7.57570i	0.356389	+	0.258932i
$857$	−17.2016	−	52.9412i	−0.587596	−	1.80844i	−0.588584	−	0.808436i	$-0.700314\pi$
$857$	−17.2016	−	52.9412i	−0.587596	−	1.80844i	0.000987578	−	1.00000i	$-0.499686\pi$
$858$	−27.4164	−	19.9192i	−0.935981	−	0.680030i
$859$	0.652476	−	2.00811i	0.0222622	−	0.0685160i	−0.939308	−	0.343074i	$-0.888532\pi$
$859$	0.652476	−	2.00811i	0.0222622	−	0.0685160i	0.961570	+	0.274558i	$0.0885317\pi$
$860$	0.236068	−	0.726543i	0.00804985	−	0.0247749i
$861$	−1.65248	−	5.08580i	−0.0563162	−	0.173324i
$862$	19.4164			0.661325
$863$	−9.81966			−0.334265			−0.167133	−	0.985934i	$-0.553451\pi$
$863$	−9.81966			−0.334265			−0.167133	+	0.985934i	$0.553451\pi$
$864$	15.1246	+	46.5488i	0.514550	+	1.58362i
$865$	−2.38197	+	1.73060i	−0.0809893	+	0.0588422i
$866$	−13.3262	−	9.68208i	−0.452844	−	0.329010i
$867$	53.1246			1.80421
$868$		0			0
$869$	−23.4164			−0.794347
$870$	11.7082	+	8.50651i	0.396945	+	0.288398i
$871$	20.9443	−	15.2169i	0.709670	−	0.515605i
$872$	9.63525	+	29.6543i	0.326291	+	1.00422i
$873$	−119.138			−4.03220
$874$	−20.6525			−0.698580
$875$	−0.656541	−	2.02063i	−0.0221951	−	0.0683096i
$876$	−5.23607	+	16.1150i	−0.176910	+	0.544474i
$877$	−5.57953	+	17.1720i	−0.188407	+	0.579858i	−0.999990	−	0.00437905i	$-0.998606\pi$
$877$	−5.57953	+	17.1720i	−0.188407	+	0.579858i	0.811583	+	0.584237i	$0.198606\pi$
$878$	1.54508	+	1.12257i	0.0521441	+	0.0378849i
$879$	0.472136	+	1.45309i	0.0159248	+	0.0490113i
$880$	7.85410	+	5.70634i	0.264762	+	0.192361i
$881$	16.4721	−	11.9677i	0.554960	−	0.403202i	−0.274651	−	0.961544i	$-0.588562\pi$
$881$	16.4721	−	11.9677i	0.554960	−	0.403202i	0.829611	+	0.558342i	$0.188562\pi$
$882$	−25.9443	+	79.8483i	−0.873589	+	2.68863i
$883$	25.7082	−	18.6781i	0.865150	−	0.628568i	−0.0641312	−	0.997941i	$-0.520428\pi$
$883$	25.7082	−	18.6781i	0.865150	−	0.628568i	0.929281	+	0.369373i	$0.120428\pi$
$884$	1.23607	−	0.898056i	0.0415735	−	0.0302049i
$885$	−2.23607	+	6.88191i	−0.0751646	+	0.231333i
$886$	−40.1976	+	29.2052i	−1.35046	+	0.981169i
$887$	−21.8992	−	15.9107i	−0.735303	−	0.534229i	0.155934	−	0.987768i	$-0.450161\pi$
$887$	−21.8992	−	15.9107i	−0.735303	−	0.534229i	−0.891237	+	0.453539i	$0.850161\pi$
$888$	−4.47214	−	13.7638i	−0.150075	−	0.461884i
$889$	−2.38197	−	1.73060i	−0.0798886	−	0.0580424i
$890$	5.85410	−	18.0171i	0.196230	−	0.603934i
$891$	15.0902	−	46.4428i	0.505540	−	1.55589i
$892$	0.763932	+	2.35114i	0.0255783	+	0.0787220i
$893$	−5.52786			−0.184983
$894$	−52.3607			−1.75120
$895$	0.527864	+	1.62460i	0.0176445	+	0.0543043i
$896$	−2.60081	+	1.88960i	−0.0868871	+	0.0631271i
$897$	−48.3607	−	35.1361i	−1.61472	−	1.17316i
$898$	−50.6525			−1.69030
$899$		0			0
$900$	−18.4721			−0.615738
$901$	6.47214	+	4.70228i	0.215618	+	0.156656i
$902$	−18.3262	+	13.3148i	−0.610197	+	0.443334i
$903$	−0.291796	−	0.898056i	−0.00971037	−	0.0298854i
$904$	−7.76393			−0.258225
$905$	−4.18034			−0.138959
$906$	22.9443	+	70.6152i	0.762272	+	2.34603i
$907$	−7.48936	+	23.0499i	−0.248680	+	0.765358i	0.746329	+	0.665577i	$0.231814\pi$
$907$	−7.48936	+	23.0499i	−0.248680	+	0.765358i	−0.995009	+	0.0997816i	$0.968186\pi$
$908$	−1.23607	+	3.80423i	−0.0410204	+	0.126248i
$909$	18.1353	+	13.1760i	0.601508	+	0.437021i
$910$	−0.381966	−	1.17557i	−0.0126620	−	0.0389698i
$911$	−14.7082	−	10.6861i	−0.487305	−	0.354047i	0.316842	−	0.948478i	$-0.397377\pi$
$911$	−14.7082	−	10.6861i	−0.487305	−	0.354047i	−0.804147	+	0.594431i	$0.797377\pi$
$912$	28.4164	−	20.6457i	0.940961	−	0.683648i
$913$	−9.23607	+	28.4257i	−0.305669	+	0.940753i
$914$	4.00000	−	2.90617i	0.132308	−	0.0961276i
$915$	21.4164	−	15.5599i	0.708005	−	0.514395i
$916$	−2.56231	+	7.88597i	−0.0846610	+	0.260560i
$917$	−2.29180	+	1.66509i	−0.0756818	+	0.0549860i
$918$	14.4721	+	10.5146i	0.477652	+	0.347034i
$919$	−4.47214	−	13.7638i	−0.147522	−	0.454027i	0.849805	−	0.527098i	$-0.176720\pi$
$919$	−4.47214	−	13.7638i	−0.147522	−	0.454027i	−0.997327	+	0.0730714i	$0.976720\pi$
$920$	10.3262	+	7.50245i	0.340446	+	0.247348i
$921$	28.7082	−	88.3548i	0.945967	−	2.91139i
$922$	17.1803	−	52.8756i	0.565804	−	1.74137i
$923$	9.18034	+	28.2542i	0.302175	+	0.929998i
$924$	−0.944272			−0.0310643
$925$	8.00000			0.263038
$926$	−1.29180	−	3.97574i	−0.0424511	−	0.130651i
$927$	−37.6976	+	27.3889i	−1.23815	+	0.899569i
$928$	7.56231	+	5.49434i	0.248245	+	0.180360i
$929$	−20.0000			−0.656179			−0.328089	−	0.944647i	$-0.606405\pi$
$929$	−20.0000			−0.656179			−0.328089	+	0.944647i	$0.606405\pi$
$930$		0			0
$931$	15.5279			0.508905
$932$	−8.97214	−	6.51864i	−0.293892	−	0.213525i
$933$	−76.3951	+	55.5043i	−2.50106	+	1.81713i
$934$	2.35410	+	7.24518i	0.0770286	+	0.237070i
$935$	1.52786			0.0499665
$936$	54.0689			1.76730
$937$	2.79837	+	8.61251i	0.0914189	+	0.281358i	0.986304	−	0.164938i	$-0.0527425\pi$
$937$	2.79837	+	8.61251i	0.0914189	+	0.281358i	−0.894885	+	0.446297i	$0.852743\pi$
$938$	0.944272	−	2.90617i	0.0308316	−	0.0948898i
$939$	−16.7639	+	51.5941i	−0.547070	+	1.68371i
$940$	−1.23607	−	0.898056i	−0.0403161	−	0.0292914i
$941$	−11.7426	−	36.1401i	−0.382799	−	1.17814i	−0.938064	−	0.346462i	$-0.887383\pi$
$941$	−11.7426	−	36.1401i	−0.382799	−	1.17814i	0.555265	−	0.831674i	$-0.312617\pi$
$942$	88.4853	+	64.2883i	2.88301	+	2.09463i
$943$	−32.3262	+	23.4864i	−1.05269	+	0.764822i
$944$	−3.35410	+	10.3229i	−0.109167	+	0.335981i
$945$	2.76393	−	2.00811i	0.0899107	−	0.0653240i
$946$	−3.23607	+	2.35114i	−0.105214	+	0.0764422i
$947$	−4.03444	+	12.4167i	−0.131102	+	0.403490i	−0.994963	−	0.100240i	$-0.968039\pi$
$947$	−4.03444	+	12.4167i	−0.131102	+	0.403490i	0.863862	+	0.503729i	$0.168039\pi$
$948$	−18.9443	+	13.7638i	−0.615281	+	0.447028i
$949$	22.1803	+	16.1150i	0.720004	+	0.523114i
$950$	4.47214	+	13.7638i	0.145095	+	0.446557i
$951$	10.6180	+	7.71445i	0.344313	+	0.250158i
$952$	−0.124612	+	0.383516i	−0.00403869	+	0.0124298i
$953$	14.1246	−	43.4711i	0.457541	−	1.40817i	−0.410585	−	0.911822i	$-0.634675\pi$
$953$	14.1246	−	43.4711i	0.457541	−	1.40817i	0.868126	−	0.496344i	$-0.165325\pi$
$954$	−39.1246	−	120.413i	−1.26671	−	3.89852i
$955$	−19.1803			−0.620661
$956$	−7.23607			−0.234031
$957$	−5.52786	−	17.0130i	−0.178690	−	0.549953i
$958$	−30.4894	+	22.1518i	−0.985066	+	0.715693i
$959$	−1.20163	−	0.873032i	−0.0388025	−	0.0281917i
$960$	−13.7082			−0.442430
$961$		0			0
$962$	10.4721			0.337635
$963$	−34.8435	−	25.3153i	−1.12281	−	0.815773i
$964$	−7.18034	+	5.21682i	−0.231263	+	0.168023i
$965$	1.07295	+	3.30220i	0.0345395	+	0.106301i
$966$	−7.05573			−0.227014
$967$	60.3607			1.94107			0.970534	−	0.240963i	$-0.0774632\pi$
$967$	60.3607			1.94107			0.970534	+	0.240963i	$0.0774632\pi$
$968$	4.83688	+	14.8864i	0.155463	+	0.478467i
$969$	1.70820	−	5.25731i	0.0548754	−	0.168889i
$970$	−7.97214	+	24.5357i	−0.255970	+	0.787794i
$971$	22.6525	+	16.4580i	0.726953	+	0.528162i	0.888598	−	0.458687i	$-0.151680\pi$
$971$	22.6525	+	16.4580i	0.726953	+	0.528162i	−0.161645	+	0.986849i	$0.551680\pi$
$972$	−6.79837	−	20.9232i	−0.218058	−	0.671113i
$973$	−2.56231	−	1.86162i	−0.0821438	−	0.0596809i
$974$	25.1803	−	18.2946i	0.806830	−	0.586196i
$975$	−12.9443	+	39.8384i	−0.414548	+	1.27585i
$976$	32.1246	−	23.3399i	1.02828	−	0.747092i
$977$	38.2254	−	27.7724i	1.22294	−	0.888518i	0.226599	−	0.973988i	$-0.427239\pi$
$977$	38.2254	−	27.7724i	1.22294	−	0.888518i	0.996341	+	0.0854705i	$0.0272393\pi$
$978$	−17.3262	+	53.3247i	−0.554032	+	1.70514i
$979$	−18.9443	+	13.7638i	−0.605462	+	0.439894i
$980$	3.47214	+	2.52265i	0.110913	+	0.0805832i
$981$	−32.1976	−	99.0939i	−1.02799	−	3.16382i
$982$	−5.70820	−	4.14725i	−0.182156	−	0.132344i
$983$	12.2148	−	37.5932i	0.389591	−	1.19904i	−0.543504	−	0.839407i	$-0.682903\pi$
$983$	12.2148	−	37.5932i	0.389591	−	1.19904i	0.933095	−	0.359631i	$-0.117097\pi$
$984$	15.6525	−	48.1734i	0.498983	−	1.53571i
$985$	3.52786	+	10.8576i	0.112407	+	0.345953i
$986$	3.41641			0.108801
$987$	−1.88854			−0.0601130
$988$	1.38197	+	4.25325i	0.0439662	+	0.135314i
$989$	−5.70820	+	4.14725i	−0.181510	+	0.131875i
$990$	−19.5623	−	14.2128i	−0.621731	−	0.451714i
$991$	−16.5410			−0.525443			−0.262721	−	0.964872i	$-0.584620\pi$
$991$	−16.5410			−0.525443			−0.262721	+	0.964872i	$0.584620\pi$
$992$		0			0
$993$	−6.47214			−0.205387
$994$	2.83688	+	2.06111i	0.0899804	+	0.0653746i
$995$	15.3262	−	11.1352i	0.485874	−	0.353008i
$996$	9.23607	+	28.4257i	0.292656	+	0.900703i
$997$	−29.3607			−0.929862			−0.464931	−	0.885347i	$-0.653921\pi$
$997$	−29.3607			−0.929862			−0.464931	+	0.885347i	$0.653921\pi$
$998$	−10.6525			−0.337198
$999$	8.94427	+	27.5276i	0.282984	+	0.870936i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.c.374.1		4
31.2	even	5		961.2.d.d.628.1		4
31.3	odd	30		961.2.g.d.235.1		8
31.4	even	5		31.2.a.a.1.2	✓	2
31.5	even	3		961.2.g.a.732.1		8
31.6	odd	6		961.2.g.d.816.1		8
31.7	even	15		961.2.c.e.439.2		4
31.8	even	5		961.2.d.d.531.1		4
31.9	even	15		961.2.g.h.844.1		8
31.10	even	15		961.2.g.h.448.1		8
31.11	odd	30		961.2.c.c.521.2		4
31.12	odd	30		961.2.g.e.846.1		8
31.13	odd	30		961.2.g.d.338.1		8
31.14	even	15		961.2.g.h.547.1		8
31.15	odd	10		961.2.d.a.388.1		4
31.16	even	5	inner	961.2.d.c.388.1		4
31.17	odd	30		961.2.g.e.547.1		8
31.18	even	15		961.2.g.a.338.1		8
31.19	even	15		961.2.g.h.846.1		8
31.20	even	15		961.2.c.e.521.2		4
31.21	odd	30		961.2.g.e.448.1		8
31.22	odd	30		961.2.g.e.844.1		8
31.23	odd	10		961.2.d.g.531.1		4
31.24	odd	30		961.2.c.c.439.2		4
31.25	even	3		961.2.g.a.816.1		8
31.26	odd	6		961.2.g.d.732.1		8
31.27	odd	10		961.2.a.f.1.2		2
31.28	even	15		961.2.g.a.235.1		8
31.29	odd	10		961.2.d.g.628.1		4
31.30	odd	2		961.2.d.a.374.1		4
93.35	odd	10		279.2.a.a.1.1		2
93.89	even	10		8649.2.a.c.1.1		2
124.35	odd	10		496.2.a.i.1.2		2
155.4	even	10		775.2.a.d.1.1		2
155.97	odd	20		775.2.b.d.249.4		4
155.128	odd	20		775.2.b.d.249.1		4
217.97	odd	10		1519.2.a.a.1.2		2
248.35	odd	10		1984.2.a.n.1.1		2
248.221	even	10		1984.2.a.r.1.2		2
341.252	odd	10		3751.2.a.b.1.1		2
372.35	even	10		4464.2.a.bf.1.1		2
403.376	even	10		5239.2.a.f.1.1		2
465.314	odd	10		6975.2.a.y.1.2		2
527.407	even	10		8959.2.a.b.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.a.a.1.2	✓	2	31.4	even	5
279.2.a.a.1.1		2	93.35	odd	10
496.2.a.i.1.2		2	124.35	odd	10
775.2.a.d.1.1		2	155.4	even	10
775.2.b.d.249.1		4	155.128	odd	20
775.2.b.d.249.4		4	155.97	odd	20
961.2.a.f.1.2		2	31.27	odd	10
961.2.c.c.439.2		4	31.24	odd	30
961.2.c.c.521.2		4	31.11	odd	30
961.2.c.e.439.2		4	31.7	even	15
961.2.c.e.521.2		4	31.20	even	15
961.2.d.a.374.1		4	31.30	odd	2
961.2.d.a.388.1		4	31.15	odd	10
961.2.d.c.374.1		4	1.1	even	1	trivial
961.2.d.c.388.1		4	31.16	even	5	inner
961.2.d.d.531.1		4	31.8	even	5
961.2.d.d.628.1		4	31.2	even	5
961.2.d.g.531.1		4	31.23	odd	10
961.2.d.g.628.1		4	31.29	odd	10
961.2.g.a.235.1		8	31.28	even	15
961.2.g.a.338.1		8	31.18	even	15
961.2.g.a.732.1		8	31.5	even	3
961.2.g.a.816.1		8	31.25	even	3
961.2.g.d.235.1		8	31.3	odd	30
961.2.g.d.338.1		8	31.13	odd	30
961.2.g.d.732.1		8	31.26	odd	6
961.2.g.d.816.1		8	31.6	odd	6
961.2.g.e.448.1		8	31.21	odd	30
961.2.g.e.547.1		8	31.17	odd	30
961.2.g.e.844.1		8	31.22	odd	30
961.2.g.e.846.1		8	31.12	odd	30
961.2.g.h.448.1		8	31.10	even	15
961.2.g.h.547.1		8	31.14	even	15
961.2.g.h.844.1		8	31.9	even	15
961.2.g.h.846.1		8	31.19	even	15
1519.2.a.a.1.2		2	217.97	odd	10
1984.2.a.n.1.1		2	248.35	odd	10
1984.2.a.r.1.2		2	248.221	even	10
3751.2.a.b.1.1		2	341.252	odd	10
4464.2.a.bf.1.1		2	372.35	even	10
5239.2.a.f.1.1		2	403.376	even	10
6975.2.a.y.1.2		2	465.314	odd	10
8649.2.a.c.1.1		2	93.89	even	10
8959.2.a.b.1.2		2	527.407	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.30902 - 0.951057i) q^{2} +(2.61803 - 1.90211i) q^{3} +(0.190983 + 0.587785i) q^{4} +1.00000 q^{5} -5.23607 q^{6} +(0.0729490 + 0.224514i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(2.30902 - 7.10642i) q^{9} +(-1.30902 - 0.951057i) q^{10} +(0.618034 + 1.90211i) q^{11} +(1.61803 + 1.17557i) q^{12} +(2.61803 - 1.90211i) q^{13} +(0.118034 - 0.363271i) q^{14} +(2.61803 - 1.90211i) q^{15} +(3.92705 - 2.85317i) q^{16} +(0.236068 - 0.726543i) q^{17} +(-9.78115 + 7.10642i) q^{18} +(1.80902 + 1.31433i) q^{19} +(0.190983 + 0.587785i) q^{20} +(0.618034 + 0.449028i) q^{21} +(1.00000 - 3.07768i) q^{22} +(1.76393 - 5.42882i) q^{23} +(2.23607 + 6.88191i) q^{24} -4.00000 q^{25} -5.23607 q^{26} +(-4.47214 - 13.7638i) q^{27} +(-0.118034 + 0.0857567i) q^{28} +(-2.23607 - 1.62460i) q^{29} -5.23607 q^{30} -3.38197 q^{32} +(5.23607 + 3.80423i) q^{33} +(-1.00000 + 0.726543i) q^{34} +(0.0729490 + 0.224514i) q^{35} +4.61803 q^{36} -2.00000 q^{37} +(-1.11803 - 3.44095i) q^{38} +(3.23607 - 9.95959i) q^{39} +(-0.690983 + 2.12663i) q^{40} +(-5.66312 - 4.11450i) q^{41} +(-0.381966 - 1.17557i) q^{42} +(-1.00000 - 0.726543i) q^{43} +(-1.00000 + 0.726543i) q^{44} +(2.30902 - 7.10642i) q^{45} +(-7.47214 + 5.42882i) q^{46} +(-2.00000 + 1.45309i) q^{47} +(4.85410 - 14.9394i) q^{48} +(5.61803 - 4.08174i) q^{49} +(5.23607 + 3.80423i) q^{50} +(-0.763932 - 2.35114i) q^{51} +(1.61803 + 1.17557i) q^{52} +(-3.23607 + 9.95959i) q^{53} +(-7.23607 + 22.2703i) q^{54} +(0.618034 + 1.90211i) q^{55} -0.527864 q^{56} +7.23607 q^{57} +(1.38197 + 4.25325i) q^{58} +(-1.80902 + 1.31433i) q^{59} +(1.61803 + 1.17557i) q^{60} +8.18034 q^{61} +1.76393 q^{63} +(-3.42705 - 2.48990i) q^{64} +(2.61803 - 1.90211i) q^{65} +(-3.23607 - 9.95959i) q^{66} +8.00000 q^{67} +0.472136 q^{68} +(-5.70820 - 17.5680i) q^{69} +(0.118034 - 0.363271i) q^{70} +(-2.83688 + 8.73102i) q^{71} +(13.5172 + 9.82084i) q^{72} +(2.61803 + 8.05748i) q^{73} +(2.61803 + 1.90211i) q^{74} +(-10.4721 + 7.60845i) q^{75} +(-0.427051 + 1.31433i) q^{76} +(-0.381966 + 0.277515i) q^{77} +(-13.7082 + 9.95959i) q^{78} +(-3.61803 + 11.1352i) q^{79} +(3.92705 - 2.85317i) q^{80} +(-19.7533 - 14.3516i) q^{81} +(3.50000 + 10.7719i) q^{82} +(12.0902 + 8.78402i) q^{83} +(-0.145898 + 0.449028i) q^{84} +(0.236068 - 0.726543i) q^{85} +(0.618034 + 1.90211i) q^{86} -8.94427 q^{87} -4.47214 q^{88} +(3.61803 + 11.1352i) q^{89} +(-9.78115 + 7.10642i) q^{90} +(0.618034 + 0.449028i) q^{91} +3.52786 q^{92} +4.00000 q^{94} +(1.80902 + 1.31433i) q^{95} +(-8.85410 + 6.43288i) q^{96} +(-4.92705 - 15.1639i) q^{97} -11.2361 q^{98} +14.9443 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} + 6 q^{3} + 3 q^{4} + 4 q^{5} - 12 q^{6} + 7 q^{7} - 5 q^{8} + 7 q^{9} - 3 q^{10} - 2 q^{11} + 2 q^{12} + 6 q^{13} - 4 q^{14} + 6 q^{15} + 9 q^{16} - 8 q^{17} - 19 q^{18} + 5 q^{19} + 3 q^{20}+ \cdots + 24 q^{99}+O(q^{100}) \) 4 * q - 3 * q^2 + 6 * q^3 + 3 * q^4 + 4 * q^5 - 12 * q^6 + 7 * q^7 - 5 * q^8 + 7 * q^9 - 3 * q^10 - 2 * q^11 + 2 * q^12 + 6 * q^13 - 4 * q^14 + 6 * q^15 + 9 * q^16 - 8 * q^17 - 19 * q^18 + 5 * q^19 + 3 * q^20 - 2 * q^21 + 4 * q^22 + 16 * q^23 - 16 * q^25 - 12 * q^26 + 4 * q^28 - 12 * q^30 - 18 * q^32 + 12 * q^33 - 4 * q^34 + 7 * q^35 + 14 * q^36 - 8 * q^37 + 4 * q^39 - 5 * q^40 - 7 * q^41 - 6 * q^42 - 4 * q^43 - 4 * q^44 + 7 * q^45 - 12 * q^46 - 8 * q^47 + 6 * q^48 + 18 * q^49 + 12 * q^50 - 12 * q^51 + 2 * q^52 - 4 * q^53 - 20 * q^54 - 2 * q^55 - 20 * q^56 + 20 * q^57 + 10 * q^58 - 5 * q^59 + 2 * q^60 - 12 * q^61 + 16 * q^63 - 7 * q^64 + 6 * q^65 - 4 * q^66 + 32 * q^67 - 16 * q^68 + 4 * q^69 - 4 * q^70 - 27 * q^71 + 25 * q^72 + 6 * q^73 + 6 * q^74 - 24 * q^75 + 5 * q^76 - 6 * q^77 - 28 * q^78 - 10 * q^79 + 9 * q^80 - 41 * q^81 + 14 * q^82 + 26 * q^83 - 14 * q^84 - 8 * q^85 - 2 * q^86 + 10 * q^89 - 19 * q^90 - 2 * q^91 + 32 * q^92 + 16 * q^94 + 5 * q^95 - 22 * q^96 - 13 * q^97 - 36 * q^98 + 24 * q^99

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